×

zbMATH — the first resource for mathematics

Ainsworth, Mark

Compute Distance To:
Author ID: ainsworth.mark Recent zbMATH articles by "Ainsworth, Mark"
Published as: Ainsworth, Mark; Ainsworth, M.
External Links: MGP
Documents Indexed: 135 Publications since 1989, including 5 Books

Publications by Year

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
682
2000
A posteriori error estimation in finite element analysis. Zbl 0895.76040
Ainsworth, Mark; Oden, J. Tinsley
211
1997
A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080
Ainsworth, Mark; Oden, J. Tinsley
160
1993
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
92
2004
Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
78
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.
69
2006
Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102
Ainsworth, Mark
61
2005
Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057
Ainsworth, Mark; Senior, Bill
53
1997
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
51
2015
A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083
Ainsworth, Mark
50
2007
A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067
Ainsworth, Mark; Oden, J. Tinsley
50
1997
A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods. Zbl 0778.73060
Ainsworth, Mark; Oden, J. Tinsley
47
1992
Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114
Ainsworth, Mark; Babuska, Ivo
44
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
43
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.
40
1993
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
40
2003
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
40
2017
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
39
2011
A preconditioner based on domain decomposition for \(h\)-\(p\) finite-element approximation on quasi-uniform meshes. Zbl 0855.65044
Ainsworth, Mark
37
1996
An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052
Ainsworth, Mark; Senior, Bill
33
1998
A posteriori error estimators in the finite element method. Zbl 0757.65109
Ainsworth, Mark; Craig, Alan
33
1992
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
32
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
32
1999
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
29
2015
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
29
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.
28
1989
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
28
2009
Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
27
2001
Local a posteriori error estimators for variational inequalities. Zbl 0768.65032
Ainsworth, Mark; Oden, J. Tinsley; Lee, C. Y.
26
1993
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
24
2005
The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
19
2000
The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122
Ainsworth, Mark; Kay, David
19
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
18
2000
Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations. Zbl 0934.76040
Ainsworth, Mark; Sherwin, Spencer
17
1999
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
17
2010
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
16
2018
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
15
2004
\(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119
Ainsworth, Mark; Pinchedez, Katia
15
2002
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
14
2005
Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
14
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.
14
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
14
1993
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
14
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
14
2007
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
13
2001
A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
13
2002
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
13
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
13
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
13
2020
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
12
2012
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
12
2011
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
12
2017
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
12
2014
A posteriori error estimation for \(h-p\) approximations in elastostatics. Zbl 0802.73072
Ainsworth, M.; Oden, J. T.; Wu, W.
11
1994
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
11
2003
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
10
2015
A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. Zbl 0860.65111
Ainsworth, Mark
10
1996
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
9
2012
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087
Ainsworth, Mark
9
1998
Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
9
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
9
2017
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
9
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
9
2011
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, W.
8
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.
8
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
8
2010
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
7
2014
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
7
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
7
2000
\(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113
Ainsworth, Mark; Senior, Bill
7
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
7
2002
The influence and selection of subspaces for a posteriori error estimators. Zbl 0873.65099
Ainsworth, Mark
7
1996
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
7
2010
Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215
Ainsworth, Mark; Rankin, Richard
7
2008
Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
6
2003
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
6
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
6
2013
Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055
Ainsworth, Mark; Arnold, Mark
5
2001
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
5
2005
The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076
Ainsworth, Mark; Pinchedez, Katia
5
2002
Three-step \(h\)-\(p\) adaptive strategy for the incompressible Navier-Stokes equations. Zbl 0844.76057
Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark
5
1995
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
5
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
5
2014
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
4
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.
4
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.)
4
2003
A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355
Ainsworth, Mark; Mihai, L. Angela
4
2006
\(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
4
2020
Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076
Ainsworth, Mark; Rankin, Richard
4
2011
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
4
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
3
2012
Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092
Ainsworth, Mark; McLean, Bill; Tran, Thanh
3
2000
Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043
Ainsworth, Mark
3
1999
Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050
Sherwin, Spencer J.; Ainsworth, Mark
3
2000
The performance of Bank-Weiser’s error estimator for quadrilateral finite elements. Zbl 0807.65109
Ainsworth, Mark
3
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.
3
1989
Modeling and numerical analysis of masonry structures. Zbl 1115.74036
Ainsworth, Mark; Mihai, L. Angela
3
2007
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
3
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.
3
2019
Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041
Ainsworth, Mark; Glusa, Christian
3
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
13
2020
\(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
4
2020
Fractional phase-field crystal modelling: analysis, approximation and pattern formation. Zbl 1443.74160
Ainsworth, Mark; Mao, Zhiping
1
2020
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
6
2019
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
5
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.
3
2019
Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
2
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
1
2019
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
16
2018
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
14
2018
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
3
2018
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
40
2017
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
12
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
9
2017
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
4
2017
Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041
Ainsworth, Mark; Glusa, Christian
3
2017
Compression using lossless decimation: analysis and application. Zbl 1420.68085
Ainsworth, Mark; Klasky, Scott; Whitney, Ben
2
2017
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
9
2016
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
7
2016
Computing the Bézier control points of the Lagrangian interpolant in arbitrary dimension. Zbl 1339.65023
Ainsworth, Mark; Sánchez, Manuel A.
2
2016
Multigrid at scale? Zbl 1352.65622
Ainsworth, Mark; Glusa, Christian
1
2016
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
51
2015
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
29
2015
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
10
2015
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
4
2015
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
12
2014
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
7
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
5
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
6
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
1
2013
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
12
2012
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
9
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
3
2012
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
39
2011
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
12
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
9
2011
Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076
Ainsworth, Mark; Rankin, Richard
4
2011
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
29
2010
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
17
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
8
2010
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
7
2010
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
28
2009
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
13
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
3
2009
An adaptive multi-scale computational modelling of Clare College Bridge. Zbl 1227.74033
Mihai, L. A.; Ainsworth, Mark
2
2009
An adaptive multi-scale approach to the modelling of masonry structures. Zbl 1183.74179
Ainsworth, Mark; Mihai, L. Angela
1
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
13
2008
Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215
Ainsworth, Mark; Rankin, Richard
7
2008
A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083
Ainsworth, Mark
50
2007
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
32
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
14
2007
Modeling and numerical analysis of masonry structures. Zbl 1115.74036
Ainsworth, Mark; Mihai, L. Angela
3
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.
69
2006
A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355
Ainsworth, Mark; Mihai, L. Angela
4
2006
Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102
Ainsworth, Mark
61
2005
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
24
2005
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
14
2005
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
5
2005
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
92
2004
Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
78
2004
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
15
2004
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
40
2003
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
11
2003
Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
9
2003
Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
6
2003
Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017
Ainsworth, Mark; Davies, Penny; Duncan, Dugald; Martin, Paul; Rynne, Bryan
4
2003
Dispersive properties of high-order finite elements. Zbl 1047.76039
Ainsworth, Mark
1
2003
\(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119
Ainsworth, Mark; Pinchedez, Katia
15
2002
A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
13
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
7
2002
The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076
Ainsworth, Mark; Pinchedez, Katia
5
2002
Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
27
2001
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
13
2001
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, W.
8
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.
8
2001
Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055
Ainsworth, Mark; Arnold, Mark
5
2001
A posteriori error estimation in finite element analysis. Zbl 1008.65076
Ainsworth, Mark; Oden, J. Tinsley
682
2000
The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
19
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
18
2000
Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
14
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
7
2000
Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092
Ainsworth, Mark; McLean, Bill; Tran, Thanh
3
2000
Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050
Sherwin, Spencer J.; Ainsworth, Mark
3
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.
1
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
32
1999
The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122
Ainsworth, Mark; Kay, David
19
1999
Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations. Zbl 0934.76040
Ainsworth, Mark; Sherwin, Spencer
17
1999
\(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113
Ainsworth, Mark; Senior, Bill
7
1999
Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043
Ainsworth, Mark
3
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
1
1999
Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114
Ainsworth, Mark; Babuska, Ivo
44
1998
An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052
Ainsworth, Mark; Senior, Bill
33
1998
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087
Ainsworth, Mark
9
1998
Semi-discrete Galerkin approximation of the single layer equation by general splines. Zbl 0909.65084
Ainsworth, Mark; Grigorieff, Rolf; Sloan, Ian
2
1998
A posteriori error estimation in finite element analysis. Zbl 0895.76040
Ainsworth, Mark; Oden, J. Tinsley
211
1997
Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057
Ainsworth, Mark; Senior, Bill
53
1997
A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067
Ainsworth, Mark; Oden, J. Tinsley
50
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.
4
1997
A preconditioner based on domain decomposition for \(h\)-\(p\) finite-element approximation on quasi-uniform meshes. Zbl 0855.65044
Ainsworth, Mark
37
1996
A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. Zbl 0860.65111
Ainsworth, Mark
10
1996
...and 15 more Documents
all top 5

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
all top 5

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
all top 5

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)

Citations by Year