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## Ainsworth, Mark

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 Author ID: ainsworth.mark Published as: Ainsworth, Mark; Ainsworth, M. External Links: MGP
 Documents Indexed: 135 Publications since 1989, including 5 Books
all top 5

#### Co-Authors

 20 single-authored 12 Oden, John Tinsley 11 Rankin, Richard 8 Glusa, Christian 5 Mao, Zhiping 5 Mihai, L. Angela 5 Senior, Bill 4 Barrenechea, Gabriel R. 4 Davydov, Oleg V. 4 Fu, Guosheng 4 Klasky, Scott 4 Parker, Charles 4 Vejchodský, Tomáš 4 Whitney, Ben 3 Allendes, Alejandro 3 Coggins, Patrick 3 Coyle, Joe 3 Craig, Alan W. 3 Demkowicz, Leszek F. 3 Dörfler, Willibald 3 Jiang, Shuai 3 Karniadakis, George Em 3 Kelly, Donald W. 3 Levesley, Jeremy 3 Marletta, Marco 3 McLean, William 3 Tuğluk, Ozan 3 Wu, Weihan 2 Andriamaro, Gaelle 2 Arnold, Mark G. 2 Guo, Benqi 2 Light, William A. 2 Pinchedez, Katia 2 Sánchez, Manuel A. 2 Sherwin, Spencer J. 2 Sloan, Ian Hugh 2 Wajid, Hafiz Abdul 2 Zayernouri, Mohsen 2 Zienkiewicz, Olgierd Cecil 1 Andrews, Derek J. 1 Babuška, Ivo 1 Cai, Wei 1 Carstensen, Carsten 1 Davies, Penny J. 1 Devloo, Philippe Remy Bernard 1 Duncan, Dugald B. 1 Durán, Omar 1 Gomes, Sônia Maria 1 Grigorieff, Rolf Dieter 1 Gulian, Mamikon 1 Guzmán, Johnny 1 Kim, Changwan 1 Lischke, Anna 1 Ma, Xinhui 1 Meerschaert, Mark Marvin 1 Monk, Peter B. 1 Muniz, Wagner Barbosa 1 Pang, Guofei 1 Rynne, Bryan P. 1 Sayas, Francisco-Javier 1 Schumaker, Larry L. 1 Song, Fangying 1 Wachtel, Andreas 1 Wang, Hongrui 1 Zheng, Xiaoning
all top 5

#### Serials

 23 Computer Methods in Applied Mechanics and Engineering 21 SIAM Journal on Numerical Analysis 15 SIAM Journal on Scientific Computing 10 Numerische Mathematik 6 IMA Journal of Numerical Analysis 5 International Journal for Numerical Methods in Engineering 4 Journal of Computational Physics 4 Applied Numerical Mathematics 3 Mathematics of Computation 3 Journal of Computational and Applied Mathematics 3 Numerical Methods for Partial Differential Equations 3 Journal of Scientific Computing 2 Computers & Mathematics with Applications 2 The ANZIAM Journal 1 Applicable Analysis 1 IMA Journal of Applied Mathematics 1 International Journal for Numerical Methods in Fluids 1 Chaos, Solitons and Fractals 1 Computing 1 Mathematische Nachrichten 1 Constructive Approximation 1 Applications of Mathematics 1 Advances in Computational Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 International Journal of Numerical Analysis and Modeling 1 Oberwolfach Reports 1 Springer Series in Computational Mathematics 1 Lecture Notes in Computational Science and Engineering 1 Numerical Mathematics and Scientific Computation 1 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts 1 Communications on Applied Mathematics and Computation
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#### Fields

 114 Numerical analysis (65-XX) 58 Partial differential equations (35-XX) 26 Fluid mechanics (76-XX) 19 Mechanics of deformable solids (74-XX) 6 Computer science (68-XX) 6 Optics, electromagnetic theory (78-XX) 5 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Information and communication theory, circuits (94-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

115 Publications have been cited 2,845 times in 1,985 Documents Cited by Year
A posteriori error estimation in finite element analysis. Zbl 1008.65076
Ainsworth, Mark; Oden, J. Tinsley
2000
A posteriori error estimation in finite element analysis. Zbl 0895.76040
Ainsworth, Mark; Oden, J. Tinsley
1997
A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080
Ainsworth, Mark; Oden, J. Tinsley
1993
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
2004
Discrete dispersion relation for $$hp$$-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
2004
Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. Zbl 1102.76032
Ainsworth, M.; Monk, P.; Muniz, W.
2006
Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102
Ainsworth, Mark
2005
Aspects of an adaptive $$hp$$-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057
Ainsworth, Mark; Senior, Bill
1997
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
2015
A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083
Ainsworth, Mark
2007
A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067
Ainsworth, Mark; Oden, J. Tinsley
1997
A procedure for a posteriori error estimation for $$h$$-$$p$$ finite element methods. Zbl 0778.73060
Ainsworth, Mark; Oden, J. Tinsley
1992
Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114
Ainsworth, Mark; Babuska, Ivo
1998
An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Zbl 0844.76056
Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark
1994
A posteriori error estimators for second order elliptic systems. II: An optimal order process for calculating self-equilibrating fluxes. Zbl 0789.65083
Ainsworth, M.; Oden, J. T.
1993
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
2003
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
2017
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
2011
A preconditioner based on domain decomposition for $$h$$-$$p$$ finite-element approximation on quasi-uniform meshes. Zbl 0855.65044
Ainsworth, Mark
1996
An adaptive refinement strategy for $$hp$$-finite element computations. Zbl 0895.65052
Ainsworth, Mark; Senior, Bill
1998
A posteriori error estimators in the finite element method. Zbl 0757.65109
Ainsworth, Mark; Craig, Alan
1992
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
2007
The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125
Ainsworth, Mark; McLean, William; Tran, Thanh
1999
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
2015
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
2010
Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method. Zbl 0716.73082
Ainsworth, M.; Zhu, J. Z.; Craig, A. W.; Zienkiewicz, O. C.
1989
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
2009
Hierachic $$hp$$-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
2001
Local a posteriori error estimators for variational inequalities. Zbl 0768.65032
Ainsworth, Mark; Oden, J. Tinsley; Lee, C. Y.
1993
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
2005
The stability of mixed $$hp$$-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
2000
The approximation theory for the $$p$$-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122
Ainsworth, Mark; Kay, David
1999
An additive Schwarz preconditioner for $$p$$-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084
Ainsworth, Mark; Guo, Benqi
2000
Domain decomposition preconditioners for $$p$$ and $$hp$$ finite element approximation of Stokes equations. Zbl 0934.76040
Ainsworth, Mark; Sherwin, Spencer
1999
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
2010
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
2018
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
2004
$$hp$$-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119
Ainsworth, Mark; Pinchedez, Katia
2002
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
2005
Approximation theory for the $$hp$$-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
2000
Solution of elastic scattering problems in linear acoustics using $$h$$-$$p$$ boundary element methods. Zbl 0770.73092
Demkowicz, L.; Oden, J. Tinsley; Ainsworth, M.; Geng, P.
1991
A posteriori error estimators for second order elliptic systems. I: Theoretical foundations and a posteriori error analysis. Zbl 0764.65060
Ainsworth, Mark; Oden, J. Tinsley
1993
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
2018
Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. Zbl 1173.76424
Ainsworth, Mark; Demkowicz, Leszek; Kim, Chang-Wan
2007
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
2001
A uniformly stable family of mixed $$hp$$-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
2002
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
2009
Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141
Ainsworth, Mark; Rankin, Richard
2008
What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em
2020
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
2012
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
2011
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
2017
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
2014
A posteriori error estimation for $$h-p$$ approximations in elastostatics. Zbl 0802.73072
Ainsworth, M.; Oden, J. T.; Wu, W.
1994
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
2003
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
2015
A hierarchical domain decomposition preconditioner for $$h$$-$$p$$ finite element approximation on locally refined meshes. Zbl 0860.65111
Ainsworth, Mark
1996
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
2012
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087
Ainsworth, Mark
1998
Conditioning of hierarchic $$p$$-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
2003
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver. Zbl 1439.65142
Ainsworth, Mark; Glusa, Christian
2017
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
2016
Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. Zbl 1208.65156
Ainsworth, Mark; Rankin, Richard
2011
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, W.
2001
A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem. Zbl 0999.65116
Ainsworth, Mark; Kelly, Donald W.
2001
Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. Zbl 1208.65155
Ainsworth, Mark; Rankin, Richard
2010
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
2014
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
2016
Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. Zbl 1049.65135
Ainsworth, Mark; Arnold, Mark
2000
$$hp$$-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113
Ainsworth, Mark; Senior, Bill
1999
Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Zbl 1022.65131
Ainsworth, Mark; Guo, Benqi
2002
The influence and selection of subspaces for a posteriori error estimators. Zbl 0873.65099
Ainsworth, Mark
1996
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
2010
Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215
Ainsworth, Mark; Rankin, Richard
2008
Computation of Maxwell eigenvalues on curvilinear domains using $$hp$$-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
2003
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
2019
On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
2013
Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055
Ainsworth, Mark; Arnold, Mark
2001
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
2005
The $$hp$$-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076
Ainsworth, Mark; Pinchedez, Katia
2002
Three-step $$h$$-$$p$$ adaptive strategy for the incompressible Navier-Stokes equations. Zbl 0844.76057
Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark
1995
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
2019
Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Zbl 1425.65140
Ainsworth, Mark; Vejchodský, Tomáš
2014
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
2017
Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem. Zbl 0890.65109
Ainsworth, M.; Kelly, D. W.; Sloan, I. H.; Wang, S. L.
1997
Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017
Ainsworth, Mark (ed.); Davies, Penny (ed.); Duncan, Dugald (ed.); Martin, Paul (ed.); Rynne, Bryan (ed.)
2003
A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355
Ainsworth, Mark; Mihai, L. Angela
2006
$$H^2$$-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
2020
Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076
Ainsworth, Mark; Rankin, Richard
2011
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
2015
Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. Zbl 1333.76050
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
2012
Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092
Ainsworth, Mark; McLean, Bill; Tran, Thanh
2000
Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043
Ainsworth, Mark
1999
Unsteady Navier-Stokes solvers using hybrid spectral/$$hp$$ element methods. Zbl 0995.76050
Sherwin, Spencer J.; Ainsworth, Mark
2000
The performance of Bank-Weiser’s error estimator for quadrilateral finite elements. Zbl 0807.65109
Ainsworth, Mark
1994
Simple and practical error estimation and adaptivity: h and h-p version procedures. Zbl 0693.73047
Zienkiewicz, O. C.; Zhu, J. Z.; Craig, A. W.; Ainsworth, M.
1989
Modeling and numerical analysis of masonry structures. Zbl 1115.74036
Ainsworth, Mark; Mihai, L. Angela
2007
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
2018
An $$\mathcal{O}(p^3)$$ $$hp$$-version FEM in two dimensions: preconditioning and post-processing. Zbl 1441.65089
Ainsworth, Mark; Jiang, Shuai; Sanchéz, Manuel A.
2019
Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041
Ainsworth, Mark; Glusa, Christian
2017
What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em
2020
$$H^2$$-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
2020
Fractional phase-field crystal modelling: analysis, approximation and pattern formation. Zbl 1443.74160
Ainsworth, Mark; Mao, Zhiping
2020
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
2019
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
2019
An $$\mathcal{O}(p^3)$$ $$hp$$-version FEM in two dimensions: preconditioning and post-processing. Zbl 1441.65089
Ainsworth, Mark; Jiang, Shuai; Sanchéz, Manuel A.
2019
Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
2019
Multilevel techniques for compression and reduction of scientific data-quantitative control of accuracy in derived quantities. Zbl 1429.68069
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
2019
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
2018
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
2018
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
2018
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
2017
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
2017
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver. Zbl 1439.65142
Ainsworth, Mark; Glusa, Christian
2017
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
2017
Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041
Ainsworth, Mark; Glusa, Christian
2017
Compression using lossless decimation: analysis and application. Zbl 1420.68085
Ainsworth, Mark; Klasky, Scott; Whitney, Ben
2017
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
2016
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
2016
Computing the Bézier control points of the Lagrangian interpolant in arbitrary dimension. Zbl 1339.65023
Ainsworth, Mark; Sánchez, Manuel A.
2016
Multigrid at scale? Zbl 1352.65622
Ainsworth, Mark; Glusa, Christian
2016
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
2015
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
2015
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
2015
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
2015
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
2014
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
2014
Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Zbl 1425.65140
Ainsworth, Mark; Vejchodský, Tomáš
2014
On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
2013
Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. Zbl 1455.65207
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
2013
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
2012
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
2012
Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. Zbl 1333.76050
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
2012
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
2011
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
2011
Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. Zbl 1208.65156
Ainsworth, Mark; Rankin, Richard
2011
Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076
Ainsworth, Mark; Rankin, Richard
2011
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
2010
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
2010
Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. Zbl 1208.65155
Ainsworth, Mark; Rankin, Richard
2010
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
2010
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
2009
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
2009
A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Zbl 1231.74429
Mihai, L. Angela; Ainsworth, Mark
2009
An adaptive multi-scale computational modelling of Clare College Bridge. Zbl 1227.74033
Mihai, L. A.; Ainsworth, Mark
2009
An adaptive multi-scale approach to the modelling of masonry structures. Zbl 1183.74179
Ainsworth, Mark; Mihai, L. Angela
2009
Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141
Ainsworth, Mark; Rankin, Richard
2008
Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215
Ainsworth, Mark; Rankin, Richard
2008
A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083
Ainsworth, Mark
2007
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
2007
Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. Zbl 1173.76424
Ainsworth, Mark; Demkowicz, Leszek; Kim, Chang-Wan
2007
Modeling and numerical analysis of masonry structures. Zbl 1115.74036
Ainsworth, Mark; Mihai, L. Angela
2007
Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. Zbl 1102.76032
Ainsworth, M.; Monk, P.; Muniz, W.
2006
A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355
Ainsworth, Mark; Mihai, L. Angela
2006
Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102
Ainsworth, Mark
2005
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
2005
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
2005
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
2005
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
2004
Discrete dispersion relation for $$hp$$-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
2004
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
2004
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
2003
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
2003
Conditioning of hierarchic $$p$$-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
2003
Computation of Maxwell eigenvalues on curvilinear domains using $$hp$$-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
2003
Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017
Ainsworth, Mark; Davies, Penny; Duncan, Dugald; Martin, Paul; Rynne, Bryan
2003
Dispersive properties of high-order finite elements. Zbl 1047.76039
Ainsworth, Mark
2003
$$hp$$-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119
Ainsworth, Mark; Pinchedez, Katia
2002
A uniformly stable family of mixed $$hp$$-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
2002
Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Zbl 1022.65131
Ainsworth, Mark; Guo, Benqi
2002
The $$hp$$-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076
Ainsworth, Mark; Pinchedez, Katia
2002
Hierachic $$hp$$-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
2001
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
2001
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, W.
2001
A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem. Zbl 0999.65116
Ainsworth, Mark; Kelly, Donald W.
2001
Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055
Ainsworth, Mark; Arnold, Mark
2001
A posteriori error estimation in finite element analysis. Zbl 1008.65076
Ainsworth, Mark; Oden, J. Tinsley
2000
The stability of mixed $$hp$$-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
2000
An additive Schwarz preconditioner for $$p$$-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084
Ainsworth, Mark; Guo, Benqi
2000
Approximation theory for the $$hp$$-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
2000
Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. Zbl 1049.65135
Ainsworth, Mark; Arnold, Mark
2000
Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092
Ainsworth, Mark; McLean, Bill; Tran, Thanh
2000
Unsteady Navier-Stokes solvers using hybrid spectral/$$hp$$ element methods. Zbl 0995.76050
Sherwin, Spencer J.; Ainsworth, Mark
2000
Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation. Zbl 0977.65093
Cao, T.; Kelly, D. W.; Ainsworth, M.
2000
The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125
Ainsworth, Mark; McLean, William; Tran, Thanh
1999
The approximation theory for the $$p$$-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122
Ainsworth, Mark; Kay, David
1999
Domain decomposition preconditioners for $$p$$ and $$hp$$ finite element approximation of Stokes equations. Zbl 0934.76040
Ainsworth, Mark; Sherwin, Spencer
1999
$$hp$$-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113
Ainsworth, Mark; Senior, Bill
1999
Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043
Ainsworth, Mark
1999
The graduate student’s guide to numerical analysis ’98. Lecture notes from the 8th EPSRC summer school in numerical analysis. Leicester, GB, July 5–17, 1998. Zbl 0920.00043
Ainsworth, Mark; Levesley, Jeremy; Marletta, Marco
1999
Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114
Ainsworth, Mark; Babuska, Ivo
1998
An adaptive refinement strategy for $$hp$$-finite element computations. Zbl 0895.65052
Ainsworth, Mark; Senior, Bill
1998
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087
Ainsworth, Mark
1998
Semi-discrete Galerkin approximation of the single layer equation by general splines. Zbl 0909.65084
Ainsworth, Mark; Grigorieff, Rolf; Sloan, Ian
1998
A posteriori error estimation in finite element analysis. Zbl 0895.76040
Ainsworth, Mark; Oden, J. Tinsley
1997
Aspects of an adaptive $$hp$$-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057
Ainsworth, Mark; Senior, Bill
1997
A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067
Ainsworth, Mark; Oden, J. Tinsley
1997
Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem. Zbl 0890.65109
Ainsworth, M.; Kelly, D. W.; Sloan, I. H.; Wang, S. L.
1997
A preconditioner based on domain decomposition for $$h$$-$$p$$ finite-element approximation on quasi-uniform meshes. Zbl 0855.65044
Ainsworth, Mark
1996
A hierarchical domain decomposition preconditioner for $$h$$-$$p$$ finite element approximation on locally refined meshes. Zbl 0860.65111
Ainsworth, Mark
1996
...and 15 more Documents
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#### Cited by 2,463 Authors

 66 Ainsworth, Mark 33 Oden, John Tinsley 31 Demkowicz, Leszek F. 31 Vohralík, Martin 28 Carstensen, Carsten 24 Praetorius, Dirk 24 Zhang, Zhimin 23 Díez, Pedro 21 Nicaise, Serge 19 Baccouch, Mahboub 18 Li, Jichun 17 Babuška, Ivo 16 Repin, Sergeĭ Igorevich 15 Huang, Yunqing 15 Huerta, Antonio 14 Heuer, Norbert 14 Karniadakis, George Em 14 Otárola, Enrique 13 Ladevèze, Pierre 12 Gudi, Thirupathi 12 Parés, Núria 11 Bespalov, Alexei 11 Calo, Victor Manuel 11 Ern, Alexandre 11 Glusa, Christian 11 Hoppe, Ronald H. W. 11 Liu, Steve Wenbin 11 Schroder, Andreas 11 Strouboulis, Theofanis 11 Wang, Hong 10 Führer, Thomas 10 Karkulik, Michael 10 Nochetto, Ricardo Horacio 10 Patera, Anthony T. 10 Picasso, Marco 10 Rankin, Richard 10 Schöberl, Joachim 10 Stein, Erwin 10 Yang, Yidu 9 Adjerid, Slimane 9 Allendes, Alejandro 9 Chan, Jesse 9 Gatica, Gabriel N. 9 Hauke, Guillermo 9 Houston, Paul 9 Merdon, Christian 9 Pardo, David 9 Rank, Ernst 9 Ródenas, Juan José 9 Sauter, Stefan A. 9 Tavener, Simon J. 9 van der Vegt, Jaap J. W. 9 Wheeler, Mary Fanett 9 Yan, Ningning 8 Bordas, Stéphane Pierre Alain 8 Carey, Graham Francis 8 Chamoin, Ludovic 8 Chaudhry, Jehanzeb Hameed 8 Creusé, Emmanuel 8 Deng, Quanling 8 Düster, Alexander 8 Estep, Donald J. 8 Feischl, Michael 8 Georgoulis, Emmanuil H. 8 Guo, Hailong 8 Kim, Kwang Yeon 8 Prudhomme, Serge 8 Rachowicz, Waldemar 8 Shephard, Mark S. 8 Stenberg, Rolf 8 Veeser, Andreas 8 Wick, Thomas 8 Wohlmuth, Barbara I. 8 Wu, Haijun 8 Xu, Yifeng 8 Zayernouri, Mohsen 8 Zhang, Shun 8 Zou, Qingsong 7 Beirão da Veiga, Lourenço 7 Beuchler, Sven 7 Bi, Hai 7 Cai, Zhiqiang 7 Du, Yu 7 Ervin, Vincent J. 7 Fuenmayor, Francisco Javier 7 Giani, Stefano 7 Hiptmair, Ralf 7 Lamichhane, Bishnu Prasad 7 Ledger, Paul David 7 Mao, Shipeng 7 Melenk, Jens Markus 7 Ovall, Jeffrey S. 7 Park, Eun-Jae 7 Rüter, Marcus Olavi 7 Schwab, Christoph 7 Sherwin, Spencer J. 7 Shi, Zhongci 7 Stephan, Ernst Peter 7 Tempone, Raúl F. 7 Vejchodský, Tomáš ...and 2,363 more Authors
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#### Cited in 162 Serials

 371 Computer Methods in Applied Mechanics and Engineering 124 Computers & Mathematics with Applications 123 Journal of Computational Physics 122 Journal of Scientific Computing 98 Journal of Computational and Applied Mathematics 92 Numerische Mathematik 84 Applied Numerical Mathematics 83 International Journal for Numerical Methods in Engineering 73 Mathematics of Computation 65 SIAM Journal on Scientific Computing 59 SIAM Journal on Numerical Analysis 46 Computational Mechanics 41 Numerical Methods for Partial Differential Equations 35 Applied Mathematics and Computation 29 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 22 Computers and Fluids 19 Advances in Computational Mathematics 19 Engineering Analysis with Boundary Elements 17 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 14 International Journal for Numerical Methods in Fluids 14 Calcolo 13 Computational Methods in Applied Mathematics 13 Journal of Numerical Mathematics 12 Communications in Numerical Methods in Engineering 11 Applied Mathematics Letters 11 Applied Mathematical Modelling 10 Mathematics and Computers in Simulation 10 Applications of Mathematics 10 Fractional Calculus & Applied Analysis 10 Archives of Computational Methods in Engineering 9 Journal of Mathematical Sciences (New York) 8 BIT 8 Numerical Linear Algebra with Applications 8 Science China. Mathematics 7 COMPEL 7 Numerical Algorithms 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Mathematical Methods in the Applied Sciences 6 Computing 6 International Journal of Computer Mathematics 6 Computational Geosciences 6 Foundations of Computational Mathematics 5 Computational and Applied Mathematics 5 Mathematical Problems in Engineering 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 Communications in Nonlinear Science and Numerical Simulation 5 Discrete and Continuous Dynamical Systems. Series B 5 Acta Numerica 5 SIAM/ASA Journal on Uncertainty Quantification 4 Journal of Integral Equations and Applications 4 Computational Mathematics and Mathematical Physics 4 International Journal of Computational Fluid Dynamics 4 Abstract and Applied Analysis 4 European Journal of Mechanics. A. Solids 4 Engineering Computations 4 International Journal of Computational Methods 4 Frontiers of Mathematics in China 4 East Asian Journal on Applied Mathematics 3 Applicable Analysis 3 Journal of Mathematical Analysis and Applications 3 Numerical Functional Analysis and Optimization 3 SIAM Journal on Control and Optimization 3 Applied Mathematics and Mechanics. (English Edition) 3 Science in China. Series A 3 SIAM Review 3 Archive of Applied Mechanics 3 Computational Optimization and Applications 3 Computing and Visualization in Science 3 Lobachevskii Journal of Mathematics 3 Journal of Applied Mathematics 3 Central European Journal of Mathematics 3 Advances in Numerical Analysis 3 Communications on Applied Mathematics and Computation 3 Electronic Research Archive 2 ACM Transactions on Mathematical Software 2 Kybernetika 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Computer Aided Geometric Design 2 Constructive Approximation 2 SIAM Journal on Matrix Analysis and Applications 2 Forum Mathematicum 2 SIAM Journal on Mathematical Analysis 2 Advances in Engineering Software 2 ETNA. Electronic Transactions on Numerical Analysis 2 Optimization Methods & Software 2 International Journal of Applied Mathematics and Computer Science 2 Nonlinear Analysis. Modelling and Control 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Advances in Difference Equations 2 Journal of Computational Acoustics 2 Boundary Value Problems 2 GAMM-Mitteilungen 2 Acta Mechanica Sinica 2 International Journal for Computational Methods in Engineering Science and Mechanics 2 International Journal for Numerical Methods in Biomedical Engineering 2 Communications in Mathematics and Statistics 2 AMM. Applied Mathematics and Mechanics. (English Edition) 2 SMAI Journal of Computational Mathematics 1 Communications on Pure and Applied Mathematics 1 International Journal of Systems Science ...and 62 more Serials
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#### Cited in 40 Fields

 1,685 Numerical analysis (65-XX) 758 Partial differential equations (35-XX) 402 Mechanics of deformable solids (74-XX) 376 Fluid mechanics (76-XX) 128 Optics, electromagnetic theory (78-XX) 103 Calculus of variations and optimal control; optimization (49-XX) 50 Ordinary differential equations (34-XX) 39 Approximations and expansions (41-XX) 35 Real functions (26-XX) 25 Probability theory and stochastic processes (60-XX) 23 Geophysics (86-XX) 22 Classical thermodynamics, heat transfer (80-XX) 20 Computer science (68-XX) 20 Statistical mechanics, structure of matter (82-XX) 18 Operator theory (47-XX) 16 Biology and other natural sciences (92-XX) 15 Integral equations (45-XX) 14 Global analysis, analysis on manifolds (58-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Special functions (33-XX) 11 Statistics (62-XX) 9 Functional analysis (46-XX) 9 Operations research, mathematical programming (90-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Systems theory; control (93-XX) 5 Potential theory (31-XX) 5 Information and communication theory, circuits (94-XX) 4 Mechanics of particles and systems (70-XX) 3 General and overarching topics; collections (00-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Difference and functional equations (39-XX) 2 History and biography (01-XX) 2 Integral transforms, operational calculus (44-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Differential geometry (53-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)