Edit Profile (opens in new tab) Houston, Paul Compute Distance To: Compute Author ID: houston.paul Published as: Houston, Paul; Houston, P. External Links: MGP Documents Indexed: 96 Publications since 1997, including 1 Book Co-Authors: 56 Co-Authors with 93 Joint Publications 1,591 Co-Co-Authors all top 5 Co-Authors 1 single-authored 21 Süli, Endre E. 14 Schötzau, Dominik 14 Wihler, Thomas Pascal 10 Antonietti, Paola Francesca 10 Hall, Edward J. C. 10 Perugia, Ilaria 9 Georgoulis, Emmanuil H. 8 Cliffe, K. Andrew 8 Giani, Stefano 8 Hartmann, Ralf 6 Congreve, Scott 4 Cangiani, Andrea 4 Schwab, Christoph 3 Collis, Joe 3 Dong, Zhaonan 3 Pennesi, Giorgio 3 Phipps, Eric T. 3 Roggendorf, Sarah 3 Salinger, Andrew G. 3 Schneebeli, Anna 3 Senior, Bill 3 van der Zee, Kristoffer George 2 Verani, Marco 1 Bain, Oliver 1 Billingham, John 1 Brezzi, Franco 1 Brownlee, Robert 1 Buffa, Annalisa 1 Facciolà, Chiara 1 Gavaghan, David J. 1 Harriman, Kathryn 1 Holton, Derek Allan 1 Hu, Xiaozhe 1 Jackson, C. P. 1 Jensen, Max 1 Joyce, Simon 1 Levesley, Jeremy 1 Lowndes, Ian S. 1 Mackenzie, John A. 1 Maini, Philip Kumar 1 Marini, Luisa Donatella 1 Mazzieri, Ilario 1 McInerney, Darragh 1 Monk, Nicholas A. M. 1 Muga, Ignacio 1 Murphy, Steven 1 Owen, Markus Roger 1 Pasquale, Liliana 1 Rannacher, Rolf 1 Robson, Janice 1 Rosswog, Stephan 1 Sarti, Marco 1 Schamberg, S. 1 Sime, Nathan 1 Smears, Iain 1 Virtanen, Juha M. 1 Ward, Michael J. 1 Warnecke, Gerald G. 1 Wei, Xiaoxi 1 Zanchetta, Pericle 1 Zhu, Liang all top 5 Serials 10 Journal of Scientific Computing 8 SIAM Journal on Scientific Computing 8 International Journal of Numerical Analysis and Modeling 7 IMA Journal of Numerical Analysis 5 Computer Methods in Applied Mechanics and Engineering 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Computers & Mathematics with Applications 3 Mathematics of Computation 3 SIAM Journal on Numerical Analysis 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Computational Physics 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 1 International Journal for Numerical Methods in Fluids 1 Journal of Engineering Mathematics 1 Bulletin of Mathematical Biology 1 Calcolo 1 Computing 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Applied Mathematics 1 Advances in Computational Mathematics 1 Computational Methods in Applied Mathematics 1 Communications in Computational Physics 1 Numerical Mathematics: Theory, Methods and Applications 1 International Journal of Computing Science and Mathematics 1 SpringerBriefs in Mathematics all top 5 Fields 81 Numerical analysis (65-XX) 46 Partial differential equations (35-XX) 30 Fluid mechanics (76-XX) 10 Optics, electromagnetic theory (78-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Mechanics of deformable solids (74-XX) 2 Approximations and expansions (41-XX) 2 Geophysics (86-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 88 Publications have been cited 2,000 times in 1,167 Documents Cited by ▼ Year ▼ Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067Houston, Paul; Schwab, Christoph; Süli, Endre 213 2002 Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Zbl 1057.76033Hartmann, Ralf; Houston, Paul 91 2002 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1298.65167Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul 84 2014 Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Zbl 1034.65081Hartmann, Ralf; Houston, Paul 75 2002 A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. Zbl 1074.65131Houston, Paul; Süli, Endre 72 2005 Energy norm a posteriori error estimation of \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems. Zbl 1116.65115Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 67 2007 Interior penalty method for the indefinite time-harmonic Maxwell equations. Zbl 1071.65155Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 56 2005 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103Houston, Paul; Schwab, Christoph; Süli, Endre 54 2000 An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Zbl 1359.76220Hartmann, Ralf; Houston, Paul 53 2008 Mixed discontinuous Galerkin approximation of the Maxwell operator. Zbl 1084.65115Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 53 2004 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1382.65307Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 48 2017 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. Zbl 1129.76030Hartmann, Ralf; Houston, Paul 45 2006 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Zbl 1084.65116Houston, Paul; Robson, Janice; Süli, Endre 44 2005 \(hp\)-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. Zbl 1029.65130Houston, Paul; Endre Süli 40 2001 \(hp\)-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1284.65163Antonietti, Paola F.; Giani, Stefano; Houston, Paul 38 2013 A posteriori error analysis for numerical approximations of Friedrichs systems. Zbl 0935.65096Houston, Paul; Mackenzie, J. A.; Süli, Endre; Warnecke, Gerald 36 1999 Discontinuous Galerkin methods for the biharmonic problem. Zbl 1176.65134Georgoulis, Emmanuil H.; Houston, Paul 34 2009 Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. Zbl 1159.65092Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 32 2007 A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods. Zbl 1230.65123Antonietti, Paola F.; Houston, Paul 30 2011 \(hp\)-version discontinous Gelerkin methods for advection-diffusion-reaction problems on polytropic meshes. Zbl 1342.65213Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 30 2016 Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. Zbl 1357.65251Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul 28 2016 Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems. Zbl 0957.65085Houston, Paul; Süli, Endre 28 2001 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. Zbl 1063.78021Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 27 2005 An \(hp\)-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity. Zbl 1118.74049Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 27 2006 A posteriori error analysis of \(hp\)-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs. Zbl 1144.65070Houston, Paul; Süli, Endre; Wihler, Thomas P. 26 2008 An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems. Zbl 1209.65124Georgoulis, Emmanuil H.; Houston, Paul; Virtanen, Juha 26 2011 \(hp\)-discontinuous Galerkin finite element methods for hyperbolic problems: Error analysis and adaptivity. Zbl 1021.76027Houston, Paul; Senior, Bill; Süli, Endre 26 2002 A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115Houston, Paul; Rannacher, Rolf; Süli, Endre 26 2000 Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. Zbl 1211.37094Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul 25 2010 Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. Zbl 1131.78007Buffa, Annalisa; Houston, Paul; Perugia, Ilaria 25 2007 Stabilised \(hp\)-finite element approximation of partial differential equations with nonnegative characteristic form. Zbl 0985.65136Houston, P.; Süli, E. 24 2001 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. II. Goal-oriented a posteriori error estimation. Zbl 1152.76429Hartmann, Ralf; Houston, Paul 23 2006 Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1421.65029Antonietti, Paola F.; Houston, Paul; Hu, Xiaozhe; Sarti, Marco; Verani, Marco 22 2017 Energy norm a posteriori error estimation for \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Zbl 1220.65156Zhu, Liang; Giani, Stefano; Houston, Paul; Schötzau, Dominik 21 2011 Adaptive finite element approximation of hyperbolic problems. Zbl 1141.76428Süli, Endre; Houston, Paul 20 2003 \(hp\)-version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. Zbl 1037.65117Harriman, Kathryn; Houston, Paul; Senior, Bill; Süli, Endre 20 2003 Sobolev regularity estimation for \(hp\)-adaptive finite element methods. Zbl 1043.65114Houston, P.; Senior, B.; Süli, E. 20 2003 A mixed DG method for linearized incompressible magnetohydrodynamics. Zbl 1203.76083Houston, Paul; Schötzau, Dominik; Wei, Xiaoxi 20 2009 \(hp\)-DGFEM for partial differential equations with nonnegative characteristic form. Zbl 0946.65102Süli, Endre; Schwab, Christoph; Houston, Paul 19 2000 Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. Zbl 1091.78017Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 18 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. Zbl 1065.76139Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 18 2005 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity. Zbl 1175.65127Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 18 2009 Modeling subgrid viscosity for advection-diffusion problems. Zbl 0980.76042Brezzi, F.; Houston, P.; Marini, D.; Süli, E. 18 2000 Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1307.65174Antonietti, Paola F.; Giani, Stefano; Houston, Paul 15 2014 Finite element methods for hyperbolic problems: A posteriori error analysis and adaptivity. Zbl 0886.65104Süli, Endre; Houston, Paul 15 1997 The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip 13 2002 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. I: A priori error analysis. Zbl 1185.65208Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 12 2007 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems. II: Strongly monotone quasi-Newtonian flows. Zbl 1457.65192Congreve, Scott; Houston, Paul; Süli, Endre; Wihler, Thomas P. 12 2013 Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods. Zbl 1435.65044Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio 12 2018 An a posteriori error indicator for discontinuous Galerkin discretizations of \(H\)(curl)-elliptic partial differential equations. Zbl 1148.65088Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 12 2007 \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1298.65173Giani, Stefano; Houston, Paul 11 2014 \(hp\)-finite element methods for hyperbolic problems. Zbl 0959.65127Süli, Endre; Houston, Paul; Schwab, Christoph 11 2000 Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. Zbl 1087.65106Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 11 2005 Anisotropic \(hp\)-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Zbl 1263.76042Giani, Stefano; Houston, Paul 10 2012 \(hp\)-discontinuous Galerkin finite element methods with least-squares stabilization. Zbl 1053.76040Houston, Paul; Jensen, Max; Süli, Endre 10 2002 A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for \(hp\)-version discontinuous Galerkin methods. Zbl 1350.65134Antonietti, Paola F.; Houston, Paul; Smears, Iain 9 2016 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Zbl 1279.65132Congreve, Scott; Houston, Paul; Wihler, Thomas P. 9 2013 Mixed \(hp\)-discontinuous Galerkin finite element methods for the Stokes problem in polygons. Zbl 1179.76053Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 9 2004 Goal-oriented a posteriori error estimation for multiple target functionals. Zbl 1064.65102Hartmann, Ralf; Houston, Paul 9 2003 An \(hp\)-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Zbl 1410.65449Houston, Paul; Wihler, Thomas P. 9 2018 \(hp\)-DGFEM for Maxwell’s equations. Zbl 1061.78012Houston, P.; Perugia, I.; Schötzau, D. 8 2003 Adaptivity and a posteriori error control for bifurcation problems. I: The Bratu problem. Zbl 1364.65246Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 7 2010 Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry. Zbl 1311.76053Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 6 2012 Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Zbl 1329.76170Giani, S.; Houston, P. 6 2014 Goal-oriented a posteriori error estimation for compressible fluid flows. Zbl 1042.76042Hartmann, R.; Houston, P. 6 2003 Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. Zbl 1311.76052Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 5 2011 An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Zbl 1442.65422Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio; Süli, Endre 5 2020 Domain decomposition preconditioners for discontinuous Galerkin discretization of compressible fluid flows. Zbl 1324.76031Giani, Stefano; Houston, Paul 4 2014 \(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Zbl 1381.76157Cliffe, K. A.; Hall, E. J. C.; Houston, P. 4 2014 Discontinuous Galerkin methods for problems with Dirac delta source. Zbl 1272.65092Houston, Paul; Wihler, Thomas Pascal 4 2012 The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin’s method. Zbl 1429.35070Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer G. 4 2019 A pre-processing moving mesh method for discontinuous Galerkin approximations of advection-diffusion-reaction problems. Zbl 1162.65403Antonietti, Paola F.; Houston, Paul 4 2008 Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation. Zbl 1447.65146Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 4 2020 Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. Zbl 1320.76066Cliffe, K. A.; Collis, J.; Houston, P. 3 2015 Adaptive discontinuous Galerkin methods on polytopic meshes. Zbl 1371.74258Collis, Joe; Houston, Paul 3 2016 Two-grid \(hp\)-DGFEM for second-order quasilinear elliptic PDEs based on an incomplete Newton iteration. Zbl 1280.65124Congreve, Scott; Houston, Paul 2 2013 Adjoint error estimation and adaptivity for hyperbolic problems. Zbl 1368.65164Houston, P. 2 2017 Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Zbl 1419.65105Congreve, Scott; Houston, Paul; Perugia, Ilaria 2 2019 Automatic symbolic computation for discontinuous Galerkin finite element methods. Zbl 1397.65268Houston, Paul; Sime, Nathan 2 2018 Adaptive energy minimisation for \(hp\)-finite element methods. Zbl 1443.65335Houston, Paul; Wihler, Thomas P. 2 2016 \(hp\)-adaptive discontinuous Galerkin methods for neutron transport criticality problems. Zbl 1385.82001Hall, Edward; Houston, Paul; Murphy, Steven 1 2017 Application of \(hp\)-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. Zbl 1273.76267Cliffe, K. A.; Hall, E. J. C.; Houston, P. 1 2013 \(hp\)-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1273.76268Congreve, S.; Houston, P.; Wihler, T. P. 1 2013 Second-order elliptic PDEs with discontinuous boundary data. Zbl 1237.65124Houston, Paul; Wihler, Thomas P. 1 2012 Adaptive discontinuous Galerkin finite element methods with interior penalty for the compressible Navier-Stokes equations. Zbl 1179.76051Hartmann, Ralf; Houston, Paul 1 2004 Output feedback control of flow separation over an aerofoil using plasma actuators. Zbl 1409.93027Broglia, R.; Choi, K.-S.; Houston, P.; Pasquale, L.; Zanchetta, P. 1 2018 High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations. Zbl 1470.86002Antonietti, Paola F.; Facciolà, Chiara; Houston, Paul; Mazzieri, Ilario; Pennesi, Giorgio; Verani, Marco 1 2021 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 07485166Congreve, Scott; Houston, Paul 1 2014 High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations. Zbl 1470.86002Antonietti, Paola F.; Facciolà, Chiara; Houston, Paul; Mazzieri, Ilario; Pennesi, Giorgio; Verani, Marco 1 2021 An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Zbl 1442.65422Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio; Süli, Endre 5 2020 Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation. Zbl 1447.65146Houston, Paul; Roggendorf, Sarah; van der Zee, Kristoffer G. 4 2020 The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin’s method. Zbl 1429.35070Houston, Paul; Muga, Ignacio; Roggendorf, Sarah; van der Zee, Kristoffer G. 4 2019 Adaptive refinement for \(hp\)-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Zbl 1419.65105Congreve, Scott; Houston, Paul; Perugia, Ilaria 2 2019 Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods. Zbl 1435.65044Antonietti, Paola F.; Houston, Paul; Pennesi, Giorgio 12 2018 An \(hp\)-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems. Zbl 1410.65449Houston, Paul; Wihler, Thomas P. 9 2018 Automatic symbolic computation for discontinuous Galerkin finite element methods. Zbl 1397.65268Houston, Paul; Sime, Nathan 2 2018 Output feedback control of flow separation over an aerofoil using plasma actuators. Zbl 1409.93027Broglia, R.; Choi, K.-S.; Houston, P.; Pasquale, L.; Zanchetta, P. 1 2018 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1382.65307Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 48 2017 Multigrid algorithms for \(hp\)-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1421.65029Antonietti, Paola F.; Houston, Paul; Hu, Xiaozhe; Sarti, Marco; Verani, Marco 22 2017 Adjoint error estimation and adaptivity for hyperbolic problems. Zbl 1368.65164Houston, P. 2 2017 \(hp\)-adaptive discontinuous Galerkin methods for neutron transport criticality problems. Zbl 1385.82001Hall, Edward; Houston, Paul; Murphy, Steven 1 2017 \(hp\)-version discontinous Gelerkin methods for advection-diffusion-reaction problems on polytropic meshes. Zbl 1342.65213Cangiani, Andrea; Dong, Zhaonan; Georgoulis, Emmanuil H.; Houston, Paul 30 2016 Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains. Zbl 1357.65251Antonietti, Paola F.; Cangiani, Andrea; Collis, Joe; Dong, Zhaonan; Georgoulis, Emmanuil H.; Giani, Stefano; Houston, Paul 28 2016 A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for \(hp\)-version discontinuous Galerkin methods. Zbl 1350.65134Antonietti, Paola F.; Houston, Paul; Smears, Iain 9 2016 Adaptive discontinuous Galerkin methods on polytopic meshes. Zbl 1371.74258Collis, Joe; Houston, Paul 3 2016 Adaptive energy minimisation for \(hp\)-finite element methods. Zbl 1443.65335Houston, Paul; Wihler, Thomas P. 2 2016 Goal-oriented a posteriori error estimation for the travel time functional in porous media flows. Zbl 1320.76066Cliffe, K. A.; Collis, J.; Houston, P. 3 2015 \(hp\)-version discontinuous Galerkin methods on polygonal and polyhedral meshes. Zbl 1298.65167Cangiani, Andrea; Georgoulis, Emmanuil H.; Houston, Paul 84 2014 Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1307.65174Antonietti, Paola F.; Giani, Stefano; Houston, Paul 15 2014 \(hp\)-adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1298.65173Giani, Stefano; Houston, Paul 11 2014 Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows. Zbl 1329.76170Giani, S.; Houston, P. 6 2014 Domain decomposition preconditioners for discontinuous Galerkin discretization of compressible fluid flows. Zbl 1324.76031Giani, Stefano; Houston, Paul 4 2014 \(hp\)-adaptive discontinuous Galerkin methods for bifurcation phenomena in open flows. Zbl 1381.76157Cliffe, K. A.; Hall, E. J. C.; Houston, P. 4 2014 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 07485166Congreve, Scott; Houston, Paul 1 2014 \(hp\)-version composite discontinuous Galerkin methods for elliptic problems on complicated domains. Zbl 1284.65163Antonietti, Paola F.; Giani, Stefano; Houston, Paul 38 2013 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems. II: Strongly monotone quasi-Newtonian flows. Zbl 1457.65192Congreve, Scott; Houston, Paul; Süli, Endre; Wihler, Thomas P. 12 2013 Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Zbl 1279.65132Congreve, Scott; Houston, Paul; Wihler, Thomas P. 9 2013 Two-grid \(hp\)-DGFEM for second-order quasilinear elliptic PDEs based on an incomplete Newton iteration. Zbl 1280.65124Congreve, Scott; Houston, Paul 2 2013 Application of \(hp\)-adaptive discontinuous Galerkin methods to bifurcation phenomena in pipe flows. Zbl 1273.76267Cliffe, K. A.; Hall, E. J. C.; Houston, P. 1 2013 \(hp\)-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. Zbl 1273.76268Congreve, S.; Houston, P.; Wihler, T. P. 1 2013 Anisotropic \(hp\)-adaptive discontinuous Galerkin finite element methods for compressible fluid flows. Zbl 1263.76042Giani, Stefano; Houston, Paul 10 2012 Adaptivity and a posteriori error control for bifurcation problems. III: Incompressible fluid flow in open systems with \(O(2)\) symmetry. Zbl 1311.76053Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 6 2012 Discontinuous Galerkin methods for problems with Dirac delta source. Zbl 1272.65092Houston, Paul; Wihler, Thomas Pascal 4 2012 Second-order elliptic PDEs with discontinuous boundary data. Zbl 1237.65124Houston, Paul; Wihler, Thomas P. 1 2012 A class of domain decomposition preconditioners for \(hp\)-discontinuous Galerkin finite element methods. Zbl 1230.65123Antonietti, Paola F.; Houston, Paul 30 2011 An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems. Zbl 1209.65124Georgoulis, Emmanuil H.; Houston, Paul; Virtanen, Juha 26 2011 Energy norm a posteriori error estimation for \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Zbl 1220.65156Zhu, Liang; Giani, Stefano; Houston, Paul; Schötzau, Dominik 21 2011 Adaptivity and a posteriori error control for bifurcation problems. II: Incompressible fluid flow in open systems with \(Z_{2}\) symmetry. Zbl 1311.76052Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 5 2011 Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. Zbl 1211.37094Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul 25 2010 Adaptivity and a posteriori error control for bifurcation problems. I: The Bratu problem. Zbl 1364.65246Cliffe, K. Andrew; Hall, Edward J. C.; Houston, Paul; Phipps, Eric T.; Salinger, Andrew G. 7 2010 Discontinuous Galerkin methods for the biharmonic problem. Zbl 1176.65134Georgoulis, Emmanuil H.; Houston, Paul 34 2009 A mixed DG method for linearized incompressible magnetohydrodynamics. Zbl 1203.76083Houston, Paul; Schötzau, Dominik; Wei, Xiaoxi 20 2009 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. II: A posteriori error analysis and adaptivity. Zbl 1175.65127Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 18 2009 An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Zbl 1359.76220Hartmann, Ralf; Houston, Paul 53 2008 A posteriori error analysis of \(hp\)-version discontinuous Galerkin finite-element methods for second-order quasi-linear elliptic PDEs. Zbl 1144.65070Houston, Paul; Süli, Endre; Wihler, Thomas P. 26 2008 A pre-processing moving mesh method for discontinuous Galerkin approximations of advection-diffusion-reaction problems. Zbl 1162.65403Antonietti, Paola F.; Houston, Paul 4 2008 Energy norm a posteriori error estimation of \(hp\)-adaptive discontinuous Galerkin methods for elliptic problems. Zbl 1116.65115Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 67 2007 Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. Zbl 1159.65092Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 32 2007 Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes. Zbl 1131.78007Buffa, Annalisa; Houston, Paul; Perugia, Ilaria 25 2007 Discontinuous Galerkin methods on \(hp\)-anisotropic meshes. I: A priori error analysis. Zbl 1185.65208Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul 12 2007 An a posteriori error indicator for discontinuous Galerkin discretizations of \(H\)(curl)-elliptic partial differential equations. Zbl 1148.65088Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 12 2007 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation. Zbl 1129.76030Hartmann, Ralf; Houston, Paul 45 2006 An \(hp\)-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity. Zbl 1118.74049Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 27 2006 Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. II. Goal-oriented a posteriori error estimation. Zbl 1152.76429Hartmann, Ralf; Houston, Paul 23 2006 A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. Zbl 1074.65131Houston, Paul; Süli, Endre 72 2005 Interior penalty method for the indefinite time-harmonic Maxwell equations. Zbl 1071.65155Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 56 2005 Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Zbl 1084.65116Houston, Paul; Robson, Janice; Süli, Endre 44 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Maxwell operator. Zbl 1063.78021Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 27 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. Zbl 1091.78017Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 18 2005 Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. Zbl 1065.76139Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 18 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator: the indefinite case. Zbl 1087.65106Houston, Paul; Perugia, Ilaria; Schneebeli, Anna; Schötzau, Dominik 11 2005 Mixed discontinuous Galerkin approximation of the Maxwell operator. Zbl 1084.65115Houston, Paul; Perugia, Ilaria; Schötzau, Dominik 53 2004 Mixed \(hp\)-discontinuous Galerkin finite element methods for the Stokes problem in polygons. Zbl 1179.76053Houston, Paul; Schötzau, Dominik; Wihler, Thomas P. 9 2004 Adaptive discontinuous Galerkin finite element methods with interior penalty for the compressible Navier-Stokes equations. Zbl 1179.76051Hartmann, Ralf; Houston, Paul 1 2004 Adaptive finite element approximation of hyperbolic problems. Zbl 1141.76428Süli, Endre; Houston, Paul 20 2003 \(hp\)-version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form. Zbl 1037.65117Harriman, Kathryn; Houston, Paul; Senior, Bill; Süli, Endre 20 2003 Sobolev regularity estimation for \(hp\)-adaptive finite element methods. Zbl 1043.65114Houston, P.; Senior, B.; Süli, E. 20 2003 Goal-oriented a posteriori error estimation for multiple target functionals. Zbl 1064.65102Hartmann, Ralf; Houston, Paul 9 2003 \(hp\)-DGFEM for Maxwell’s equations. Zbl 1061.78012Houston, P.; Perugia, I.; Schötzau, D. 8 2003 Goal-oriented a posteriori error estimation for compressible fluid flows. Zbl 1042.76042Hartmann, R.; Houston, P. 6 2003 Discontinuous \(hp\)-finite element methods for advection-diffusion-reaction problems. Zbl 1015.65067Houston, Paul; Schwab, Christoph; Süli, Endre 213 2002 Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. Zbl 1057.76033Hartmann, Ralf; Houston, Paul 91 2002 Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws. Zbl 1034.65081Hartmann, Ralf; Houston, Paul 75 2002 \(hp\)-discontinuous Galerkin finite element methods for hyperbolic problems: Error analysis and adaptivity. Zbl 1021.76027Houston, Paul; Senior, Bill; Süli, Endre 26 2002 The dynamics and pinning of a spike for a reaction-diffusion system. Zbl 1032.35029Ward, Michael J.; McInerney, Darragh; Houston, Paul; Gavaghan, David; Maini, Philip 13 2002 \(hp\)-discontinuous Galerkin finite element methods with least-squares stabilization. Zbl 1053.76040Houston, Paul; Jensen, Max; Süli, Endre 10 2002 \(hp\)-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. Zbl 1029.65130Houston, Paul; Endre Süli 40 2001 Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems. Zbl 0957.65085Houston, Paul; Süli, Endre 28 2001 Stabilised \(hp\)-finite element approximation of partial differential equations with nonnegative characteristic form. Zbl 0985.65136Houston, P.; Süli, E. 24 2001 Stabilized \(hp\)-finite element methods for first-order hyperbolic problems. Zbl 0957.65103Houston, Paul; Schwab, Christoph; Süli, Endre 54 2000 A posteriori error analysis for stabilised finite element approximations of transport problems. Zbl 0970.65115Houston, Paul; Rannacher, Rolf; Süli, Endre 26 2000 \(hp\)-DGFEM for partial differential equations with nonnegative characteristic form. Zbl 0946.65102Süli, Endre; Schwab, Christoph; Houston, Paul 19 2000 Modeling subgrid viscosity for advection-diffusion problems. Zbl 0980.76042Brezzi, F.; Houston, P.; Marini, D.; Süli, E. 18 2000 \(hp\)-finite element methods for hyperbolic problems. Zbl 0959.65127Süli, Endre; Houston, Paul; Schwab, Christoph 11 2000 A posteriori error analysis for numerical approximations of Friedrichs systems. Zbl 0935.65096Houston, Paul; Mackenzie, J. A.; Süli, Endre; Warnecke, Gerald 36 1999 Finite element methods for hyperbolic problems: A posteriori error analysis and adaptivity. Zbl 0886.65104Süli, Endre; Houston, Paul 15 1997 all cited Publications top 5 cited Publications all top 5 Cited by 1,507 Authors 41 Houston, Paul 37 Antonietti, Paola Francesca 26 Giani, Stefano 26 Li, Jichun 25 Dolejší, Vít 25 Schötzau, Dominik 21 Wihler, Thomas Pascal 20 Georgoulis, Emmanuil H. 18 Verani, Marco 15 Dumbser, Michael 14 Perugia, Ilaria 13 Feistauer, Miloslav 13 Huang, Yunqing 12 Cangiani, Andrea 12 Ern, Alexandre 12 Gudi, Thirupathi 12 Liu, Tiegang 12 Süli, Endre E. 11 Beirão da Veiga, Lourenço 11 Schwab, Christoph 10 Adjerid, Slimane 10 Baccouch, Mahboub 10 Cockburn, Bernardo 10 Di Pietro, Daniele Antonio 10 Fidkowski, Krzysztof J. 10 Mascotto, Lorenzo 10 Mazzieri, Ilario 10 Nataraj, Neela 9 Banz, Lothar 9 Cheng, Jian 9 Chung, Tsz Shun Eric 9 Stamm, Benjamin 8 Burman, Erik 8 Demkowicz, Leszek F. 8 Dong, Zhaonan 8 Mora, David 8 Pryer, Tristan 8 Vohralík, Martin 8 Wheeler, Mary Fanett 7 Brenner, Susanne Cecelia 7 Carstensen, Carsten 7 Giesselmann, Jan 7 Hall, Edward J. C. 7 Hiptmair, Ralf 7 Manzini, Gianmarco 7 May, Georg 7 Mu, Lin 7 Quarteroni, Alfio M. 7 Rui, Hongxing 7 Schroder, Andreas 7 van der Vegt, Jaap J. W. 7 Wei, Juncheng 7 Yang, Wei 7 Ye, Xiu 6 Abdulle, Assyr 6 Bertoluzza, Silvia 6 Bi, Chunjia 6 Brezzi, Franco 6 Fu, Hongfei 6 Gassner, Gregor J. 6 Gatica, Gabriel N. 6 Hartmann, Ralf 6 He, Yinnian 6 Huang, Xuehai 6 Kuzmin, Dmitri 6 Lube, Gert 6 Marini, Luisa Donatella 6 Müller, Siegfried 6 Munz, Claus-Dieter 6 Nicaise, Serge 6 Pani, Amiya Kumar 6 Rivière, Beatrice M. 6 Russo, Alessandro 6 Takizawa, Kenji 6 Tavener, Simon J. 6 Tezduyar, Tayfun E. 6 Yue, Huiqiang 6 Zhang, Shangyou 6 Zhang, Zhimin 6 Zhu, Hongqiang 5 Badia, Santiago 5 Bastian, Peter 5 Bustinza, Rommel A. 5 Chapelier, Jean-Baptiste 5 Chernov, Alexey 5 Codina, Ramon 5 Darmofal, David L. 5 de la Llave Plata, Marta 5 Dedner, Andreas S. 5 Endtmayer, Bernhard 5 Feng, Xiaobing 5 Grubišić, Luka 5 Hughes, Thomas J. R. 5 Lanteri, Stéphane 5 Larson, Mats G. 5 Lovadina, Carlo 5 Masud, Arif 5 Mavriplis, Dimitri J. 5 Mei, Liquan 5 Park, Eun-Jae ...and 1,407 more Authors all top 5 Cited in 132 Serials 133 Journal of Computational Physics 103 Computer Methods in Applied Mechanics and Engineering 103 Journal of Scientific Computing 68 Computers & Mathematics with Applications 66 Journal of Computational and Applied Mathematics 56 Applied Numerical Mathematics 48 Mathematics of Computation 44 Computers and Fluids 42 Numerische Mathematik 38 SIAM Journal on Scientific Computing 34 Applied Mathematics and Computation 30 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 30 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 29 SIAM Journal on Numerical Analysis 28 Numerical Methods for Partial Differential Equations 13 Calcolo 13 Advances in Computational Mathematics 12 Computational Mechanics 12 Communications in Computational Physics 11 Computational Methods in Applied Mathematics 11 Journal of Numerical Mathematics 10 International Journal for Numerical Methods in Fluids 9 BIT 8 International Journal for Numerical Methods in Engineering 8 International Journal of Numerical Analysis and Modeling 7 Mathematics and Computers in Simulation 6 Computational Geosciences 6 Communications on Applied Mathematics and Computation 5 Numerical Functional Analysis and Optimization 5 Numerical Algorithms 5 International Journal of Computer Mathematics 5 Engineering Analysis with Boundary Elements 5 Advances in Applied Mathematics and Mechanics 4 Applied Mathematics Letters 4 Applications of Mathematics 4 Foundations of Computational Mathematics 4 East Asian Journal on Applied Mathematics 3 Applicable Analysis 3 Journal of Differential Equations 3 Computational Optimization and Applications 3 Numerical Linear Algebra with Applications 3 Mathematical Problems in Engineering 3 Computing and Visualization in Science 3 International Journal of Computational Fluid Dynamics 3 Archives of Computational Methods in Engineering 3 Multiscale Modeling & Simulation 3 International Journal for Numerical Methods in Biomedical Engineering 3 Results in Applied Mathematics 2 Computer Physics Communications 2 Mathematical Methods in the Applied Sciences 2 Bulletin of Mathematical Biology 2 Meccanica 2 COMPEL 2 European Journal of Applied Mathematics 2 Communications in Partial Differential Equations 2 Journal of Nonlinear Science 2 Communications in Numerical Methods in Engineering 2 Abstract and Applied Analysis 2 International Journal of Theoretical and Applied Finance 2 Central European Journal of Mathematics 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 ACM Transactions on Mathematical Software 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 Acta Applicandae Mathematicae 1 Computer Aided Geometric Design 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Journal of Dynamics and Differential Equations 1 Advances in Engineering Software 1 Calculus of Variations and Partial Differential Equations 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Journal of Difference Equations and Applications 1 Journal of Inequalities and Applications 1 European Journal of Mechanics. B. Fluids 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Engineering Computations 1 Combustion Theory and Modelling 1 Lobachevskii Journal of Mathematics 1 The ANZIAM Journal 1 Matematicheskoe Modelirovanie 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics 1 Sādhanā 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of Applied Mathematics and Computing 1 Bulletin of the Brazilian Mathematical Society. New Series ...and 32 more Serials all top 5 Cited in 39 Fields 1,021 Numerical analysis (65-XX) 519 Partial differential equations (35-XX) 338 Fluid mechanics (76-XX) 116 Optics, electromagnetic theory (78-XX) 112 Mechanics of deformable solids (74-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 20 Biology and other natural sciences (92-XX) 14 Statistical mechanics, structure of matter (82-XX) 13 Ordinary differential equations (34-XX) 13 Classical thermodynamics, heat transfer (80-XX) 8 Integral equations (45-XX) 8 Probability theory and stochastic processes (60-XX) 8 Computer science (68-XX) 8 Geophysics (86-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Approximations and expansions (41-XX) 7 Operator theory (47-XX) 6 Potential theory (31-XX) 6 Functional analysis (46-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Statistics (62-XX) 5 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Differential geometry (53-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of particles and systems (70-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year