## Ern, Alexandre

Compute Distance To:
 Author ID: ern.alexandre Published as: Ern, Alexandre; Ern, A.
 Documents Indexed: 183 Publications since 1993, including 8 Books 6 Contributions as Editor Co-Authors: 103 Co-Authors with 177 Joint Publications 2,166 Co-Co-Authors
all top 5

### Co-Authors

 5 single-authored 27 Burman, Erik 22 Vohralík, Martin 21 Di Pietro, Daniele Antonio 19 Guermond, Jean-Luc 11 Giovangigli, Vincent 8 Lelièvre, Tony 8 Piperno, Serge 7 Cicuttin, Matteo 6 Bonelle, Jérôme 6 Doyen, David 5 El Alaoui, Linda 5 Lemaire, Simon 5 Smears, Iain 5 Smooke, Mitchell D. 4 Bongiovanni, Emmanuel 4 Casenave, Fabien 4 Chaumont-Frelet, Théophile 4 Delay, Guillaume 4 Glinsky-Olivier, Nathalie 4 Monasse, Laurent 4 Mozolevsky, Igor E. 4 Pignet, Nicolas 3 Braack, Malte 3 Cantin, Pierre 3 Durán, Omar 3 Formaggia, Luca 3 Le Maître, Olivier P. 3 Mariotti, Christian 3 Perotto, Simona 3 Proft, Jennifer 3 Stephansen, Annette F. 3 Tryoen, J. 2 Abbas, Mickaël 2 Achchab, Boujemaa 2 Bouchut, François 2 Calo, Victor Manuel 2 Carstensen, Carsten 2 Cascavita, Karol L. 2 Chouly, Franz 2 Daniel, Patrik 2 Deng, Quanling 2 Dolejší, Vít 2 Douglas, Craig C. 2 Ehrlacher, Virginie 2 El Fatini, Mohamed 2 Fernández, Miguel Ángel 2 Gudi, Thirupathi 2 Joubaud, Rémi 2 Lusso, Christelle 2 Mangeney, Anne 2 Marazzato, Frédéric 2 Meunier, Sébastien 2 Milani, Riccardo 2 Ndjinga, Michaël 2 Puscas, Maria Adela 2 Riedlbeck, Rita 2 Schieweck, Friedhelm 2 Souissi, Ali 2 Tenaud, Christian 2 Veneziani, Alessandro 1 Beirão da Veiga, Lourenço 1 Benaceur, Amina 1 Bertrand, Fleurianne 1 Bleyer, Jérémy 1 Boffi, Daniele 1 Boiveau, Thomas 1 Bourlioux, Anne 1 Caplain, Gilbert 1 Chalhoub, Nancy 1 Chateau, Xavier 1 Chazel, Florent 1 Cockburn, Bernardo 1 Contento, Lorenzo 1 Croisille, Jean-Pierre 1 Daru, Virginie 1 Debiane, L. 1 Djadel, Karim 1 Dong, Zhaonan 1 Dormieux, Luc 1 Droniou, Jéroôme 1 Duquennoi, Christian 1 Farin, Maxime 1 Granet, Sylvie 1 Guermond, J.-J. 1 Hédin, Florent 1 Ivorra, Benjamin 1 Kazymyrenko, Kyrylo 1 Keyes, David Elliot 1 Linke, Alexander 1 Mohammadi, Bijan 1 Muga, Ignacio 1 Nicaise, Serge 1 Nouy, Anthony 1 Pichot, Géraldine 1 Pitsch, Heinz 1 Puttkammer, Sophie 1 Quartapelle, Luigi 1 Radu, Florin Adrian 1 Roche, Olivier 1 Rojas, Sergio ...and 15 more Co-Authors
all top 5

### Serials

 16 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 14 SIAM Journal on Numerical Analysis 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Computer Methods in Applied Mechanics and Engineering 9 IMA Journal of Numerical Analysis 8 Journal of Computational Physics 8 SIAM Journal on Scientific Computing 7 Mathematics of Computation 6 Computers & Mathematics with Applications 6 Computational Methods in Applied Mathematics 4 Journal of Scientific Computing 3 Journal of Computational and Applied Mathematics 3 Computational Mechanics 3 Applied Mathematics Letters 3 Combustion Theory and Modelling 3 Multiscale Modeling & Simulation 3 Texts in Applied Mathematics 2 International Journal for Numerical Methods in Fluids 2 International Journal for Numerical Methods in Engineering 2 Numerische Mathematik 2 Numerical Methods for Partial Differential Equations 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Mathématiques & Applications (Berlin) 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Transport Theory and Statistical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Calcolo 1 Computer Aided Geometric Design 1 Journal of Computational Mathematics 1 Physica D 1 European Journal of Mechanics. B. Fluids 1 Communications in Partial Differential Equations 1 Linear Algebra and its Applications 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Computational Optimization and Applications 1 Advances in Computational Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série II. Fascicule b 1 International Journal of Computational Fluid Dynamics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Theoretical and Applied Finance 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Computational Geosciences 1 Journal of Numerical Mathematics 1 Communications in Mathematical Sciences 1 International Journal of Numerical Analysis and Modeling 1 Oberwolfach Reports 1 Applied Mathematical Sciences 1 Lecture Notes in Physics. New Series m: Monographs 1 Series in Contemporary Applied Mathematics CAM 1 Matapli 1 SEMA SIMAI Springer Series 1 SpringerBriefs in Mathematics 1 Communications on Applied Mathematics and Computation
all top 5

### Fields

 148 Numerical analysis (65-XX) 86 Partial differential equations (35-XX) 69 Fluid mechanics (76-XX) 25 Mechanics of deformable solids (74-XX) 14 Classical thermodynamics, heat transfer (80-XX) 7 Functional analysis (46-XX) 6 General and overarching topics; collections (00-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Optics, electromagnetic theory (78-XX) 5 Geophysics (86-XX) 5 Biology and other natural sciences (92-XX) 4 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Probability theory and stochastic processes (60-XX) 2 Operations research, mathematical programming (90-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

### Citations contained in zbMATH Open

159 Publications have been cited 3,418 times in 2,060 Documents Cited by Year
Theory and practice of finite elements. Zbl 1059.65103
Ern, Alexandre; Guermond, Jean-Luc
2004
Mathematical aspects of discontinuous Galerkin methods. Zbl 1231.65209
Di Pietro, Daniele Antonio; Ern, Alexandre
2012
A hybrid high-order locking-free method for linear elasticity on general meshes. Zbl 1423.74876
Di Pietro, Daniele A.; Ern, Alexandre
2015
An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Zbl 1304.65248
Di Pietro, Daniele A.; Ern, Alexandre; Lemaire, Simon
2014
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
2016
Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. Zbl 1312.76026
Ern, Alexandre; Vohralík, Martin
2015
Continuous interior penalty $$hp$$-finite element methods for advection and advection-diffusion equations. Zbl 1118.65118
Burman, Erik; Ern, Alexandre
2007
A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. Zbl 1165.65074
Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo
2009
Discontinuous Galerkin methods for Friedrichs’ systems. I: General theory. Zbl 1122.65111
Ern, A.; Guermond, J.-L.
2006
Hybrid high-order methods for variable-diffusion problems on general meshes. (Méthodes hybrides d’ordre élevé pour des problèmes à diffusion variable sur des maillages généraux.) Zbl 1308.65196
Di Pietro, Daniele A.; Ern, Alexandre
2015
A posteriori control of modeling errors and discretization errors. Zbl 1050.65100
Braack, Malte; Ern, Alexandre
2003
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
2013
Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. Zbl 1369.76024
Di Pietro, Daniele A.; Ern, Alexandre
2010
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. Zbl 1190.65165
Ern, Alexandre; Stephansen, Annette F.; Vohralík, Martin
2010
Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence. Zbl 1078.65088
Burman, Erik; Ern, Alexandre
2005
Finite element quasi-interpolation and best approximation. Zbl 1378.65041
Ern, Alexandre; Guermond, Jean-Luc
2017
Multicomponent transport algorithms. Zbl 0820.76002
Ern, Alexandre; Giovangigli, Vincent
1994
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. Zbl 1197.65013
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A.
2010
Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes. Zbl 1049.65128
Burman, Erik; Ern, Alexandre
2004
A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying. Zbl 1142.76036
Ern, A.; Piperno, S.; Djadel, K.
2008
Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation. Zbl 1101.76354
Burman, Erik; Ern, Alexandre
2002
Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures. Zbl 1231.76143
Ern, A.; Mozolevski, I.; Schuh, L.
2010
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Zbl 1230.65118
El Alaoui, Linda; Ern, Alexandre; Vohralík, Martin
2011
Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes. Zbl 1297.65132
Bonelle, Jérôme; Ern, Alexandre
2014
A discontinuous-skeletal method for advection-diffusion-reaction on general meshes. Zbl 1457.65194
Di Pietro, Daniele A.; Droniou, Jéroôme; Ern, Alexandre
2015
An accurate $$\mathbf H$$(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
2007
Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems. Zbl 1226.65086
Burman, Erik; Ern, Alexandre; Fernández, Miguel A.
2010
Discontinuous Galerkin methods for anisotropic semidefinite diffusion with advection. Zbl 1165.49032
Di Pietro, Daniele A.; Ern, Alexandre; Guermond, Jean-Luc
2008
Thermal diffusion effects in hydrogen-air and methane-air flames. Zbl 0944.76092
Ern, Alexandre; Giovangigli, Vincent
1998
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
2010
Fast and accurate multicomponent transport property evaluation. Zbl 0938.76097
Ern, Alexandre; Giovangigli, Vincent
1995
Time-integration schemes for the finite element dynamic Signorini problem. Zbl 1315.74019
Doyen, David; Ern, Alexandre; Piperno, Serge
2011
Discontinuous Galerkin methods for Friedrichs’ systems. II: Second-order elliptic PDEs. Zbl 1133.65098
Ern, Alexandre; Guermond, Jean-Luc
2006
An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrich’ systems. (An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrichs’ systems.) Zbl 1118.47003
Ern, Alexandre; Guermond, Jean-Luc; Caplain, Gilbert
2007
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2013
An unfitted hybrid high-order method for elliptic interface problems. Zbl 1448.65201
Burman, Erik; Ern, Alexandre
2018
Towards polyalgorithmic linear system solvers for nonlinear elliptic problems. Zbl 0807.65027
Ern, Alexandre; Giovangigli, Vincent; Keyes, David E.; Smooke, Mitchell D.
1994
Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws. Zbl 1273.35330
Tryoen, J.; Le Maître, O.; Ern, A.
2012
Projective iterative algorithms with application to multicomponent transport. Zbl 0867.65017
Ern, Alexandre; Giovangigli, Vincent
1997
Mollification in strongly Lipschitz domains with application to continuous and discrete de Rham complexes. Zbl 1329.65041
Ern, Alexandre; Guermond, Jean-Luc
2016
Evaluation of the condition number in linear systems arising in finite element approximations. Zbl 1149.65306
Ern, Alexandre; Guermond, Jean-Luc
2006
Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes. Zbl 1329.76249
Bonelle, Jérôme; Ern, Alexandre
2015
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
2009
A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems. Zbl 1166.76036
Ern, Alexandre; Meunier, Sébastien
2009
Hierarchical local model reduction for elliptic problems: A domain decomposition approach. Zbl 1206.65251
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro
2010
$$hp$$-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2016
A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations. Zbl 1084.65092
Ern, Alexandre; Proft, Jennifer
2005
A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods. Zbl 1174.65034
Ern, Alexandre; Stephansen, Annette F.
2008
A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods. Zbl 1357.65258
Di Pietro, Daniele A.; Ern, Alexandre; Lemaire, Simon
2016
Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. Zbl 1471.74076
Cicuttin, M.; Di Pietro, D. A.; Ern, A.
2018
Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian. Zbl 1152.65073
Burman, Erik; Ern, Alexandre
2008
Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows. Zbl 1227.76045
Sochala, P.; Ern, A.; Piperno, S.
2009
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. Zbl 1378.65165
Ern, Alexandre; Smears, Iain; VohralÍk, Martin
2017
Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes. Zbl 1433.65285
Di Pietro, Daniele A.; Ern, Alexandre
2017
A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations. Zbl 1112.65109
El Alaoui, L.; Ern, A.; Burman, E.
2007
Discontinuous Galerkin methods for Friedrichs’ systems. Part III. Multifield theories with partial coercivity. Zbl 1179.65145
Ern, Alexandre; Guermond, Jean-Luc
2008
A discontinuous skeletal method for the viscosity-dependent Stokes problem. Zbl 1436.76022
Di Pietro, Daniele A.; Ern, Alexandre; Linke, Alexander; Schieweck, Friedhelm
2016
Hybrid high-order methods for finite deformations of hyperelastic materials. Zbl 1459.74020
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2018
Éléments finis: théorie, applications, mise en œuvre. (Finite elements: Theory, applications, implementation.) Zbl 0993.65123
Ern, Alexandre; Guermond, Jean-Luc
2002
Vorticity-velocity formulation for three-dimensional steady compressible flows. Zbl 0783.76059
Ern, A.; Smooke, M. D.
1993
Weighting the edge stabilization. Zbl 1280.65095
Ern, Alexandre; Guermond, Jean-Luc
2013
Hierarchical model reduction for advection-diffusion-reaction problems. Zbl 1157.65487
Ern, A.; Perotto, S.; Veneziani, A.
2008
Coupling multimodelling with local mesh refinement for the numerical computation of laminar flames. Zbl 1068.80534
Braack, Malte; Ern, Alexandre
2004
Roe solver with entropy corrector for uncertain hyperbolic systems. Zbl 1197.65129
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A.
2010
A nonintrusive reduced basis method applied to aeroacoustic simulations. Zbl 1338.76049
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony
2015
Nonconforming finite element methods with subgrid viscosity applied to advection-diffusion-reaction equations. Zbl 1104.65110
El Alaoui, Linda; Ern, Alexandre
2006
Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions. Zbl 1409.65068
Ern, Alexandre; Guermond, Jean-Luc
2018
Spectral approximation of elliptic operators by the hybrid high-order method. Zbl 1422.65359
Calo, Victor; Cicuttin, Matteo; Deng, Quanling; Ern, Alexandre
2019
Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. Zbl 1417.65197
Bonelle, Jérôme; Di Pietro, Daniele A.; Ern, Alexandre
2015
Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods. Zbl 1077.65113
El Alaoui, Linda; Ern, Alexandre
2004
A double-layer Boussinesq-type model for highly nonlinear and dispersive waves. Zbl 1186.35156
Chazel, F.; Benoit, M.; Ern, A.; Piperno, S.
2009
Accurate velocity reconstruction for discontinuous Galerkin approximations of two-phase porous medium flows. Zbl 1162.76027
Ern, Alexandre; Mozolevski, Igor; Schuh, L.
2009
Stable broken $$H^1$$ and $$H(\operatorname{div})$$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Zbl 1434.65253
Ern, Alexandre; Vohralík, Martin
2020
Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem. Zbl 1398.76097
Burman, Erik; Ern, Alexandre; Fernández, Miguel A.
2017
Mathematical study of non-ideal electrostatic correlations in equilibrium electrolytes. Zbl 1245.35125
Ern, Alexandre; Joubaud, Rémi; Lelièvre, Tony
2012
A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry. Zbl 1184.76829
Debiane, L.; Ivorra, B.; Mohammadi, B.; Nicoud, F.; Poinsot, T.; Ern, A.; Pitsch, H.
2006
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
2013
Finite elements II. Galerkin approximation, elliptic and mixed PDEs. Zbl 1476.65002
Ern, Alexandre; Guermond, Jean-Luc
2021
Discrete $$p$$-robust $$\boldsymbol H(\mathrm{div})$$-liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ source terms. Zbl 1378.65173
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2017
Stress and flux reconstruction in Biot’s poro-elasticity problem with application to a posteriori error analysis. Zbl 1370.76086
Riedlbeck, Rita; Di Pietro, Daniele A.; Ern, Alexandre; Granet, Sylvie; Kazymyrenko, Kyrylo
2017
Numerical study of a three-dimensional chemical vapor deposition reactor with detailed chemistry. Zbl 0853.76091
Ern, Alexandre; Giovangigli, Vincent; Smooke, Mitchell D.
1996
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method. Zbl 1288.65157
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony
2014
Bunsen flame simulation by finite elements on adaptively refined, unstructured triangulations. Zbl 1068.80536
Burman, Erik; Ern, Alexandre; Giovangigli, Vincent
2004
The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders $$p \geqslant 2$$. Zbl 1128.65061
Burman, Erik; Ern, Alexandre; Mozolevski, Igor; Stamm, Benjamin
2007
An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. Zbl 1475.65186
Burman, Erik; Cicuttin, Matteo; Delay, Guillaume; Ern, Alexandre
2021
A hybrid high-order discretization combined with Nitsche’s method for contact and Tresca friction in small strain elasticity. Zbl 1452.65328
Chouly, Franz; Ern, Alexandre; Pignet, Nicolas
2020
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain. Zbl 1349.76184
Casenave, Fabien; Ern, Alexandre; Sylvand, Guillaume
2014
Volume viscosity of dilute polyatomic gas mixtures. Zbl 0869.76075
Ern, Alexandre; Giovangigli, Vincent
1995
Vorticity-velocity formulations of the Stokes problem in 3D. Zbl 0939.35144
Ern, A.; Guermond, J.-J.; Quartapelle, L.
1999
Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs. Zbl 1416.65348
Ern, Alexandre; Schieweck, Friedhelm
2016
Preface. Zbl 1349.00239
2016
Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions. Zbl 1267.65178
Di Pietro, Daniele A.; Ern, Alexandre
2012
Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. Zbl 1281.65123
Burman, Erik; Ern, Alexandre
2012
A hybrid high-order method for incremental associative plasticity with small deformations. Zbl 1440.74368
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2019
Finite elements I. Approximation and interpolation. Zbl 1476.65003
Ern, Alexandre; Guermond, Jean-Luc
2020
An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms. Zbl 1436.65173
Calo, Victor M.; Ern, Alexandre; Muga, Ignacio; Rojas, Sergio
2020
A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations. Zbl 1173.65350
Achchab, B.; El Fatini, M.; Ern, A.; Souissi, A.
2009
A unified framework for a posteriori error estimation in elliptic and parabolic problems with application to finite volumes. Zbl 1246.65162
Ern, Alexandre; Vohralıḱ, Martin
2011
Convergence of a space semi-discrete modified mass method for the dynamic Signorini problem. Zbl 1245.74045
Doyen, D.; Ern, A.
2009
Continuous interior penalty $$hp$$-finite element methods for transport operators. Zbl 1119.65406
Burman, Erik; Ern, Alexandre
2006
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal $$hp$$ approximation estimates in $$\boldsymbol{H}(\operatorname{div})$$. Zbl 07524708
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin
2022
Finite elements II. Galerkin approximation, elliptic and mixed PDEs. Zbl 1476.65002
Ern, Alexandre; Guermond, Jean-Luc
2021
An unfitted hybrid high-order method with cell agglomeration for elliptic interface problems. Zbl 1475.65186
Burman, Erik; Cicuttin, Matteo; Delay, Guillaume; Ern, Alexandre
2021
Convergence analysis of hybrid high-order methods for the wave equation. Zbl 1480.65248
Burman, Erik; Duran, Omar; Ern, Alexandre; Steins, Morgane
2021
Finite elements III. First-order and time-dependent PDEs. Zbl 1457.65001
Ern, Alexandre; Guermond, Jean-Luc
2021
Hybrid high-order methods. A primer with applications to solid mechanics. Zbl 1475.74002
Cicuttin, Matteo; Ern, Alexandre; Pignet, Nicolas
2021
On the derivation of guaranteed and $$p$$-robust a posteriori error estimates for the Helmholtz equation. Zbl 07387428
Chaumont-Frelet, T.; Ern, A.; Vohralík, M.
2021
A hybrid high-order method for flow simulations in discrete fracture networks. Zbl 1471.65196
Hédin, Florent; Pichot, Géraldine; Ern, Alexandre
2021
SoftFEM: revisiting the spectral finite element approximation of second-order elliptic operators. Zbl 07419173
Deng, Quanling; Ern, Alexandre
2021
Stable broken $$H^1$$ and $$H(\operatorname{div})$$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Zbl 1434.65253
Ern, Alexandre; Vohralík, Martin
2020
A hybrid high-order discretization combined with Nitsche’s method for contact and Tresca friction in small strain elasticity. Zbl 1452.65328
Chouly, Franz; Ern, Alexandre; Pignet, Nicolas
2020
Finite elements I. Approximation and interpolation. Zbl 1476.65003
Ern, Alexandre; Guermond, Jean-Luc
2020
An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms. Zbl 1436.65173
Calo, Victor M.; Ern, Alexandre; Muga, Ignacio; Rojas, Sergio
2020
Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions. Zbl 1466.65183
Cascavita, Karol L.; Chouly, Franz; Ern, Alexandre
2020
An adaptive $$hp$$-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor. Zbl 1441.65095
Daniel, Patrik; Ern, Alexandre; Vohralík, Martin
2020
Polynomial-degree-robust $$\boldsymbol H(\mathbf{curl})$$-stability of discrete minimization in a tetrahedron. Zbl 1456.65156
Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin
2020
A quasi-optimal variant of the hybrid high-order method for elliptic partial differential equations with $$H^{-1}$$ loads. Zbl 1466.65224
Ern, Alexandre; Zanotti, Pietro
2020
Compatible discrete operator schemes for the steady incompressible Stokes and Navier-Stokes equations. Zbl 1454.65134
Bonelle, Jérôme; Ern, Alexandre; Milani, Riccardo
2020
Hybrid high-order methods for the elliptic obstacle problem. Zbl 1436.65176
Cicuttin, Matteo; Ern, Alexandre; Gudi, Thirupathi
2020
Spectral approximation of elliptic operators by the hybrid high-order method. Zbl 1422.65359
Calo, Victor; Cicuttin, Matteo; Deng, Quanling; Ern, Alexandre
2019
A hybrid high-order method for incremental associative plasticity with small deformations. Zbl 1440.74368
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2019
A hybrid high-order method for highly oscillatory elliptic problems. Zbl 1434.65246
Cicuttin, Matteo; Ern, Alexandre; Lemaire, Simon
2019
Equilibrated flux a posteriori error estimates in $$L^2(H^1)$$-norms for high-order discretizations of parabolic problems. Zbl 1467.65092
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2019
Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. Zbl 1422.65250
Boiveau, Thomas; Ehrlacher, Virginie; Ern, Alexandre; Nouy, Anthony
2019
An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. Zbl 1440.65274
Marazzato, Frédéric; Ern, Alexandre; Mariotti, Christian; Monasse, Laurent
2019
An unfitted hybrid high-order method for elliptic interface problems. Zbl 1448.65201
Burman, Erik; Ern, Alexandre
2018
Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. Zbl 1471.74076
Cicuttin, M.; Di Pietro, D. A.; Ern, A.
2018
Hybrid high-order methods for finite deformations of hyperelastic materials. Zbl 1459.74020
Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas
2018
Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions. Zbl 1409.65068
Ern, Alexandre; Guermond, Jean-Luc
2018
A progressive reduced basis/empirical interpolation method for nonlinear parabolic problems. Zbl 1397.65180
Benaceur, Amina; Ehrlacher, Virginie; Ern, Alexandre; Meunier, Sébastien
2018
An adaptive $$hp$$-refinement strategy with computable guaranteed bound on the error reduction factor. Zbl 1427.65356
Daniel, Patrik; Ern, Alexandre; Smears, Iain; Vohralík, Martin
2018
Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell’s equations. Zbl 1401.65132
Ern, Alexandre; Guermond, Jean-Luc
2018
Hybrid discretization methods with adaptive yield surface detection for Bingham pipe flows. Zbl 1407.65141
Cascavita, Karol L.; Bleyer, Jérémy; Chateau, Xavier; Ern, Alexandre
2018
Numerical methods for PDEs. State of the art techniques. Zbl 1402.65007
2018
On the implementation of a multiscale hybrid high-order method. Zbl 1456.65158
Cicuttin, Matteo; Ern, Alexandre; Lemaire, Simon
2018
Finite element quasi-interpolation and best approximation. Zbl 1378.65041
Ern, Alexandre; Guermond, Jean-Luc
2017
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. Zbl 1378.65165
Ern, Alexandre; Smears, Iain; VohralÍk, Martin
2017
Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes. Zbl 1433.65285
Di Pietro, Daniele A.; Ern, Alexandre
2017
Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem. Zbl 1398.76097
Burman, Erik; Ern, Alexandre; Fernández, Miguel A.
2017
Discrete $$p$$-robust $$\boldsymbol H(\mathrm{div})$$-liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ source terms. Zbl 1378.65173
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2017
Stress and flux reconstruction in Biot’s poro-elasticity problem with application to a posteriori error analysis. Zbl 1370.76086
Riedlbeck, Rita; Di Pietro, Daniele A.; Ern, Alexandre; Granet, Sylvie; Kazymyrenko, Kyrylo
2017
Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse. Zbl 1375.74020
Lusso, Christelle; Ern, Alexandre; Bouchut, François; Mangeney, Anne; Farin, Maxime; Roche, Olivier
2017
An edge-based scheme on polyhedral meshes for vector advection-reaction equations. Zbl 1402.65151
Cantin, Pierre; Ern, Alexandre
2017
Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis. Zbl 1390.74187
Riedlbeck, Rita; Di Pietro, Daniele A.; Ern, Alexandre
2017
A nonlinear consistent penalty method weakly enforcing positivity in the finite element approximation of the transport equation. Zbl 1439.76053
Burman, Erik; Ern, Alexandre
2017
Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. Zbl 1341.65045
Cockburn, Bernardo; Di Pietro, Daniele A.; Ern, Alexandre
2016
Mollification in strongly Lipschitz domains with application to continuous and discrete de Rham complexes. Zbl 1329.65041
Ern, Alexandre; Guermond, Jean-Luc
2016
$$hp$$-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2016
A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods. Zbl 1357.65258
Di Pietro, Daniele A.; Ern, Alexandre; Lemaire, Simon
2016
A discontinuous skeletal method for the viscosity-dependent Stokes problem. Zbl 1436.76022
Di Pietro, Daniele A.; Ern, Alexandre; Linke, Alexander; Schieweck, Friedhelm
2016
Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs. Zbl 1416.65348
Ern, Alexandre; Schieweck, Friedhelm
2016
Preface. Zbl 1349.00239
2016
A converse to Fortin’s lemma in Banach spaces. (Une réciproque au lemme de Fortin dans les espaces de Banach.) Zbl 1387.47004
Ern, Alexandre; Guermond, Jean-Luc
2016
Variants of the empirical interpolation method: symmetric formulation, choice of norms and rectangular extension. Zbl 1337.65014
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony
2016
Vertex-based compatible discrete operator schemes on polyhedral meshes for advection-diffusion equations. Zbl 1336.65184
Cantin, Pierre; Ern, Alexandre
2016
A vertex-based scheme on polyhedral meshes for advection-reaction equations with sub-mesh stabilization. Zbl 1368.65248
Cantin, Pierre; Bonelle, Jérôme; Burman, Erik; Ern, Alexandre
2016
A hybrid high-order locking-free method for linear elasticity on general meshes. Zbl 1423.74876
Di Pietro, Daniele A.; Ern, Alexandre
2015
Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. Zbl 1312.76026
Ern, Alexandre; Vohralík, Martin
2015
Hybrid high-order methods for variable-diffusion problems on general meshes. (Méthodes hybrides d’ordre élevé pour des problèmes à diffusion variable sur des maillages généraux.) Zbl 1308.65196
Di Pietro, Daniele A.; Ern, Alexandre
2015
A discontinuous-skeletal method for advection-diffusion-reaction on general meshes. Zbl 1457.65194
Di Pietro, Daniele A.; Droniou, Jéroôme; Ern, Alexandre
2015
Analysis of compatible discrete operator schemes for the Stokes equations on polyhedral meshes. Zbl 1329.76249
Bonelle, Jérôme; Ern, Alexandre
2015
A nonintrusive reduced basis method applied to aeroacoustic simulations. Zbl 1338.76049
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony
2015
Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes. Zbl 1417.65197
Bonelle, Jérôme; Di Pietro, Daniele A.; Ern, Alexandre
2015
Equilibrated tractions for the hybrid high-order method. (Tranctions équilibrées pour la méthode hybride d’ordre élevé.) Zbl 1310.65143
Di Pietro, Daniele A.; Ern, Alexandre
2015
A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation. Zbl 1320.90079
Contento, Lorenzo; Ern, Alexandre; Vermiglio, Rossana
2015
A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure. Zbl 1352.76075
Puscas, Maria Adela; Monasse, Laurent; Ern, Alexandre; Tenaud, Christian; Mariotti, Christian; Daru, Virginie
2015
A conservative embedded boundary method for an inviscid compressible flow coupled with a fragmenting structure. Zbl 1352.76074
Puscas, Maria Adela; Monasse, Laurent; Ern, Alexandre; Tenaud, Christian; Mariotti, Christian
2015
An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Zbl 1304.65248
Di Pietro, Daniele A.; Ern, Alexandre; Lemaire, Simon
2014
Analysis of compatible discrete operator schemes for elliptic problems on polyhedral meshes. Zbl 1297.65132
Bonelle, Jérôme; Ern, Alexandre
2014
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method. Zbl 1288.65157
Casenave, Fabien; Ern, Alexandre; Lelièvre, Tony
2014
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain. Zbl 1349.76184
Casenave, Fabien; Ern, Alexandre; Sylvand, Guillaume
2014
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
2013
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2013
Weighting the edge stabilization. Zbl 1280.65095
Ern, Alexandre; Guermond, Jean-Luc
2013
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
2013
Quasi-explicit time-integration schemes for dynamic fracture with set-valued cohesive zone models. Zbl 1319.74024
Doyen, D.; Ern, A.; Piperno, S.
2013
Mathematical aspects of discontinuous Galerkin methods. Zbl 1231.65209
Di Pietro, Daniele Antonio; Ern, Alexandre
2012
Adaptive anisotropic spectral stochastic methods for uncertain scalar conservation laws. Zbl 1273.35330
Tryoen, J.; Le Maître, O.; Ern, A.
2012
Mathematical study of non-ideal electrostatic correlations in equilibrium electrolytes. Zbl 1245.35125
Ern, Alexandre; Joubaud, Rémi; Lelièvre, Tony
2012
Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions. Zbl 1267.65178
Di Pietro, Daniele A.; Ern, Alexandre
2012
Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. Zbl 1281.65123
Burman, Erik; Ern, Alexandre
2012
Corrigendum to “Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures”. Zbl 1354.76104
Ern, A.; Mozolevski, I.; Schuh, L.
2012
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Zbl 1230.65118
El Alaoui, Linda; Ern, Alexandre; Vohralík, Martin
2011
Time-integration schemes for the finite element dynamic Signorini problem. Zbl 1315.74019
Doyen, David; Ern, Alexandre; Piperno, Serge
2011
A unified framework for a posteriori error estimation in elliptic and parabolic problems with application to finite volumes. Zbl 1246.65162
Ern, Alexandre; Vohralıḱ, Martin
2011
Analysis of the modified mass method for the dynamic Signorini problem with Coulomb friction. Zbl 1298.74179
Doyen, David; Ern, Alexandre
2011
A posteriori error estimates for unsteady convection-diffusion-reaction problems and the finite volume method. Zbl 1246.65210
Chalhoub, Nancy; Ern, Alexandre; Sayah, Tony; Vohralıḱ, Martin
2011
Numerical study of a thin liquid film flowing down an inclined wavy plane. Zbl 1366.76011
Ern, Alexandre; Joubaud, Rémi; Lelièvre, Tony
2011
Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations. Zbl 1369.76024
Di Pietro, Daniele A.; Ern, Alexandre
2010
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. Zbl 1190.65165
Ern, Alexandre; Stephansen, Annette F.; Vohralík, Martin
2010
Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems. Zbl 1197.65013
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A.
2010
Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures. Zbl 1231.76143
Ern, A.; Mozolevski, I.; Schuh, L.
2010
Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for first-order linear PDE systems. Zbl 1226.65086
Burman, Erik; Ern, Alexandre; Fernández, Miguel A.
2010
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
2010
Hierarchical local model reduction for elliptic problems: A domain decomposition approach. Zbl 1206.65251
Perotto, Simona; Ern, Alexandre; Veneziani, Alessandro
2010
Roe solver with entropy corrector for uncertain hyperbolic systems. Zbl 1197.65129
Tryoen, J.; Le Maître, O.; Ndjinga, M.; Ern, A.
2010
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces. Zbl 1192.74355
Doyen, David; Ern, Alexandre; Piperno, Serge
2010
A posteriori error estimation for subgrid flamelet models. Zbl 1407.76041
Bourlioux, Anne; Ern, Alexandre; Turbis, Pascal
2010
A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity. Zbl 1165.65074
Ern, Alexandre; Stephansen, Annette F.; Zunino, Paolo
2009
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
2009
...and 59 more Documents
all top 5

### Cited by 2,676 Authors

 81 Ern, Alexandre 59 Burman, Erik 58 Di Pietro, Daniele Antonio 49 Vohralík, Martin 25 Droniou, Jérôme 22 Beirão da Veiga, Lourenço 22 Salgado, Abner J. 21 Antonietti, Paola Francesca 21 Otárola, Enrique 20 Giovangigli, Vincent 19 Badia, Santiago 18 Larson, Mats G. 17 Barrenechea, Gabriel R. 17 Carstensen, Carsten 16 Georgoulis, Emmanuil H. 16 Rivière, Beatrice M. 15 Guermond, Jean-Luc 15 Smooke, Mitchell D. 15 Verani, Marco 14 Giani, Stefano 14 Linke, Alexander 14 Quarteroni, Alfio M. 14 Ye, Xiu 14 Yuan, Guangwei 13 Allendes, Alejandro 13 Botti, Lorenzo 13 Feng, Minfu 13 Hansbo, Peter 13 Langer, Ulrich 13 Mora, David 13 Oyarzúa, Ricardo 13 Wick, Thomas 13 Wihler, Thomas Pascal 12 Manzini, Gianmarco 12 Mu, Lin 12 Park, Eun-Jae 12 Perotto, Simona 12 Stamm, Benjamin 11 Codina, Ramon 11 Gatica, Gabriel N. 11 Houston, Paul 11 John, Volker 11 Maday, Yvon 11 Nochetto, Ricardo Horacio 11 Valentin, Frédéric 11 Zhang, Shangyou 10 Bennett, Beth Anne V. 10 Botti, Michele 10 Cangiani, Andrea 10 Cockburn, Bernardo 10 Dassi, Franco 10 Dolejší, Vít 10 Guillén González, Francisco M. 10 Mascotto, Lorenzo 10 Peterseim, Daniel 10 Pryer, Tristan 10 Renard, Yves 10 Zhao, Lina 9 Becker, Roland 9 Calo, Victor Manuel 9 Chaumont-Frelet, Théophile 9 Chouly, Franz 9 Chung, Tsz Shun Eric 9 Guzmán, Johnny 9 Lehrenfeld, Christoph 9 Lovadina, Carlo 9 Marche, Fabien 9 Massing, André 9 Nicaise, Serge 9 Reusken, Arnold 9 Rhebergen, Sander 9 Ruiz-Baier, Ricardo 9 Russo, Alessandro 9 Scovazzi, Guglielmo 9 Sheng, Zhiqiang 9 Shu, Chi-Wang 9 Veneziani, Alessandro 9 Zunino, Paolo 8 Ainsworth, Mark 8 Bernardi, Christine 8 Bochev, Pavel B. 8 Braack, Malte 8 Burazin, Krešimir 8 Cancès, Clément 8 Deng, Quanling 8 Eymard, Robert 8 Formaggia, Luca 8 Gutiérrez-Santacreu, Juan Vicente 8 Korotov, Sergey 8 Lipnikov, Konstantin N. 8 Meddahi, Salim 8 Ovall, Jeffrey S. 8 Qiu, Weifeng 8 Smears, Iain 8 Van Brummelen, Harald 8 Wheeler, Mary Fanett 8 Zhang, Qiang 7 Abgrall, Rémi 7 Achchab, Boujemaa 7 Antonić, Nenad ...and 2,576 more Authors
all top 5

### Cited in 205 Serials

 216 Computer Methods in Applied Mechanics and Engineering 144 Journal of Computational Physics 142 Journal of Scientific Computing 112 SIAM Journal on Numerical Analysis 102 Computers & Mathematics with Applications 94 SIAM Journal on Scientific Computing 93 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 87 Numerische Mathematik 85 Mathematics of Computation 79 Journal of Computational and Applied Mathematics 39 Applied Numerical Mathematics 37 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 34 Computational Methods in Applied Mathematics 33 Computers and Fluids 29 Combustion Theory and Modelling 28 Applied Mathematics and Computation 28 Calcolo 24 Comptes Rendus. Mathématique. Académie des Sciences, Paris 23 Numerical Methods for Partial Differential Equations 22 Computational Mechanics 22 Advances in Computational Mathematics 22 Computational Geosciences 20 International Journal for Numerical Methods in Engineering 17 Communications in Computational Physics 13 Journal of Numerical Mathematics 12 Journal of Fluid Mechanics 12 BIT 11 International Journal for Numerical Methods in Fluids 9 Mathematics and Computers in Simulation 9 Applied Mathematics Letters 9 Numerical Algorithms 9 Applied Mathematical Modelling 9 Archives of Computational Methods in Engineering 9 Multiscale Modeling & Simulation 8 Computational and Applied Mathematics 8 Advances in Applied Mathematics and Mechanics 8 SMAI Journal of Computational Mathematics 8 Communications on Applied Mathematics and Computation 7 SIAM Journal on Control and Optimization 7 ETNA. Electronic Transactions on Numerical Analysis 7 Discrete and Continuous Dynamical Systems. Series B 6 Computational Optimization and Applications 6 Foundations of Computational Mathematics 6 International Journal of Numerical Analysis and Modeling 6 S$$\vec{\text{e}}$$MA Journal 5 Physica A 5 Japan Journal of Industrial and Applied Mathematics 5 International Journal of Computer Mathematics 5 International Journal of Computational Fluid Dynamics 5 Acta Numerica 5 Kinetic and Related Models 4 Journal of Mathematical Analysis and Applications 4 Mathematical Methods in the Applied Sciences 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Journal of Computational Mathematics 4 Applications of Mathematics 4 Linear Algebra and its Applications 4 Discrete and Continuous Dynamical Systems 4 Mathematical Problems in Engineering 4 Journal of Applied Mathematics and Computing 4 SIAM Journal on Imaging Sciences 4 GEM - International Journal on Geomathematics 4 Electronic Research Archive 3 Journal of Differential Equations 3 Journal of Optimization Theory and Applications 3 Communications in Partial Differential Equations 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Physics of Fluids 3 Numerical Linear Algebra with Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 European Journal of Mechanics. B. Fluids 3 Flow, Turbulence and Combustion 3 Communications in Nonlinear Science and Numerical Simulation 3 Nonlinear Analysis. Real World Applications 3 Communications on Pure and Applied Analysis 3 Inverse Problems and Imaging 3 Science China. Mathematics 3 Evolution Equations and Control Theory 3 SIAM/ASA Journal on Uncertainty Quantification 2 Fluid Dynamics 2 International Journal of Heat and Mass Transfer 2 Inverse Problems 2 Journal of Engineering Mathematics 2 Nonlinearity 2 Transport Theory and Statistical Physics 2 Wave Motion 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Applied Mathematics and Mechanics. (English Edition) 2 Chinese Annals of Mathematics. Series B 2 Acta Applicandae Mathematicae 2 Physica D 2 Computational Mathematics and Mathematical Physics 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 SIAM Journal on Optimization 2 Journal of Mathematical Imaging and Vision 2 Continuum Mechanics and Thermodynamics 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Journal of Convex Analysis ...and 105 more Serials
all top 5

### Cited in 43 Fields

 1,668 Numerical analysis (65-XX) 878 Partial differential equations (35-XX) 772 Fluid mechanics (76-XX) 265 Mechanics of deformable solids (74-XX) 95 Classical thermodynamics, heat transfer (80-XX) 83 Calculus of variations and optimal control; optimization (49-XX) 77 Optics, electromagnetic theory (78-XX) 49 Biology and other natural sciences (92-XX) 46 Geophysics (86-XX) 45 Statistical mechanics, structure of matter (82-XX) 24 Ordinary differential equations (34-XX) 22 Functional analysis (46-XX) 22 Computer science (68-XX) 20 Operator theory (47-XX) 15 Probability theory and stochastic processes (60-XX) 15 Operations research, mathematical programming (90-XX) 14 Global analysis, analysis on manifolds (58-XX) 13 Approximations and expansions (41-XX) 13 Systems theory; control (93-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Statistics (62-XX) 11 Dynamical systems and ergodic theory (37-XX) 9 Integral equations (45-XX) 9 Mechanics of particles and systems (70-XX) 8 Real functions (26-XX) 6 General and overarching topics; collections (00-XX) 6 Potential theory (31-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Combinatorics (05-XX) 5 Differential geometry (53-XX) 4 Quantum theory (81-XX) 4 Relativity and gravitational theory (83-XX) 4 Astronomy and astrophysics (85-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Manifolds and cell complexes (57-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Convex and discrete geometry (52-XX)