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Author ID: ainsworth.mark Recent zbMATH articles by "Ainsworth, Mark"
Published as: Ainsworth, Mark; Ainsworth, M.
External Links: MGP

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Citations contained in zbMATH Open

134 Publications have been cited 3,956 times in 2,731 Documents Cited by Year
A posteriori error estimation in finite element analysis. Zbl 1008.65076
Ainsworth, Mark; Oden, J. Tinsley
882
2000
A posteriori error estimation in finite element analysis. Zbl 0895.76040
Ainsworth, Mark; Oden, J. Tinsley
278
1997
A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080
Ainsworth, Mark; Oden, J. Tinsley
181
1993
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
157
2020
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
124
2004
Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
104
2004
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
96
2017
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.
86
2006
A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em.
74
2015
Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102
Ainsworth, Mark
73
2005
A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083
Ainsworth, Mark
68
2007
Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057
Ainsworth, Mark; Senior, Bill
61
1997
A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067
Ainsworth, Mark; Oden, J. Tinsley
59
1997
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
58
2011
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
53
2017
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
52
2003
A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods. Zbl 0778.73060
Ainsworth, Mark; Oden, J. Tinsley
51
1992
An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Zbl 0844.76056
Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark
50
1994
Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114
Ainsworth, Mark; Babuska, Ivo
48
1998
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
47
2015
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
44
2018
The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125
Ainsworth, Mark; McLean, William; Tran, Thanh
42
1999
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.
42
1993
A preconditioner based on domain decomposition for \(h\)-\(p\) finite-element approximation on quasi-uniform meshes. Zbl 0855.65044
Ainsworth, Mark
42
1996
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
41
2009
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
41
2010
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
40
2007
A posteriori error estimators in the finite element method. Zbl 0757.65109
Ainsworth, Mark; Craig, Alan
38
1992
An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052
Ainsworth, Mark; Senior, Bill
38
1998
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.
34
1989
Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
30
2001
Local a posteriori error estimators for variational inequalities. Zbl 0768.65032
Ainsworth, Mark; Oden, J. Tinsley; Lee, C. Y.
30
1993
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
29
2005
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
29
2018
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
28
2017
The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122
Ainsworth, Mark; Kay, David
25
1999
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
24
2001
An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084
Ainsworth, Mark; Guo, Benqi
21
2000
The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
20
2000
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
20
2010
Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141
Ainsworth, Mark; Rankin, Richard
20
2008
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
19
2004
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
19
2013
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
19
2012
Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations. Zbl 0934.76040
Ainsworth, Mark; Sherwin, Spencer
18
1999
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
18
2005
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
17
2011
\(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119
Ainsworth, Mark; Pinchedez, Katia
16
2002
Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
16
2000
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
15
2010
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.
15
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
15
1993
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
15
2003
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
15
2007
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
15
2014
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
14
2009
A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
14
2002
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
13
2012
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
13
2016
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
13
2014
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
12
2015
Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
12
2003
Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017
12
2003
A posteriori error estimation for \(h-p\) approximations in elastostatics. Zbl 0802.73072
Ainsworth, M.; Oden, J. T.; Wu, W.
12
1994
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
11
2019
A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. Zbl 0860.65111
Ainsworth, Mark
11
1996
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
10
2018
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
10
2016
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
10
2014
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.
10
2019
A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087
Ainsworth, Mark
9
1998
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
On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
9
2013
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
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, W.
8
2001
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
8
2010
The influence and selection of subspaces for a posteriori error estimators. Zbl 0873.65099
Ainsworth, Mark
8
1996
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
8
2019
\(hp\)-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
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
Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
7
2003
Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215
Ainsworth, Mark; Rankin, Richard
7
2008
Galerkin neural networks: a framework for approximating variational equations with error control. Zbl 1486.65238
Ainsworth, Mark; Dong, Justin
7
2021
High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions. Zbl 1441.65096
Devloo, Philippe R. B.; Durán, Omar; Gomes, Sônia M.; Ainsworth, Mark
7
2019
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
6
2015
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
6
2005
Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. I: Uniform stability. Zbl 1465.76049
Ainsworth, Mark; Parker, Charles
6
2021
Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076
Ainsworth, Mark; Rankin, Richard
6
2011
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
6
2012
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
6
2017
The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076
Ainsworth, Mark; Pinchedez, Katia
6
2002
\(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
6
2020
Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055
Ainsworth, Mark; Arnold, Mark
5
2001
Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. II: Optimal convergence. Zbl 1465.76050
Ainsworth, Mark; Parker, Charles
5
2021
Three-step \(h\)-\(p\) adaptive strategy for the incompressible Navier-Stokes equations. Zbl 0844.76057
Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark
5
1995
Unlocking the secrets of locking: finite element analysis in planar linear elasticity. Zbl 1507.74441
Ainsworth, Mark; Parker, Charles
5
2022
Fractional phase-field crystal modelling: analysis, approximation and pattern formation. Zbl 1443.74160
Ainsworth, Mark; Mao, Zhiping
5
2020
Bernstein-Bézier bases for tetrahedral finite elements. Zbl 1440.65168
Ainsworth, Mark; Fu, Guosheng
5
2018
Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043
Ainsworth, Mark
4
1999
Unlocking the secrets of locking: finite element analysis in planar linear elasticity. Zbl 1507.74441
Ainsworth, Mark; Parker, Charles
5
2022
A mass conserving mixed \(hp\)-FEM scheme for Stokes flow. III: Implementation and preconditioning. Zbl 1492.65296
Ainsworth, Mark; Parker, Charles
2
2022
Active neuron least squares: a training method for multivariate rectified neural networks. Zbl 1492.65157
Ainsworth, Mark; Shin, Yeonjong
1
2022
Galerkin neural networks: a framework for approximating variational equations with error control. Zbl 1486.65238
Ainsworth, Mark; Dong, Justin
7
2021
Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. I: Uniform stability. Zbl 1465.76049
Ainsworth, Mark; Parker, Charles
6
2021
Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. II: Optimal convergence. Zbl 1465.76050
Ainsworth, Mark; Parker, Charles
5
2021
Preconditioning the mass matrix for high order finite element approximation on tetrahedra. Zbl 1466.65174
Ainsworth, Mark; Jiang, Shuai
4
2021
Preconditioning high order \(H^2\) conforming finite elements on triangles. Zbl 1472.65138
Ainsworth, Mark; Parker, Charles
4
2021
Plateau phenomenon in gradient descent training of RELU networks: explanation, quantification, and avoidance. Zbl 1487.65070
Ainsworth, Mark; Shin, Yeonjong
1
2021
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
157
2020
\(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020
Ainsworth, Mark; Parker, Charles
6
2020
Fractional phase-field crystal modelling: analysis, approximation and pattern formation. Zbl 1443.74160
Ainsworth, Mark; Mao, Zhiping
5
2020
Some remarks on spectral convergence and stability of iso-geometric analysis. Zbl 1506.65234
Ainsworth, Mark; Davydov, Oleg; Wang, Hongrui
3
2020
Multilevel techniques for compression and reduction of scientific data – the unstructured case. Zbl 1440.65169
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
1
2020
Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168
Ainsworth, Mark; Jiang, Shuai
11
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.
10
2019
A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090
Ainsworth, Mark; Vejchodský, Tomáš
8
2019
High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions. Zbl 1441.65096
Devloo, Philippe R. B.; Durán, Omar; Gomes, Sônia M.; Ainsworth, Mark
7
2019
Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
4
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
2
2019
Analysis and approximation of gradient flows associated with a fractional order Gross-Pitaevskii free energy. Zbl 1449.65302
Ainsworth, Mark; Mao, Zhiping
1
2019
Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation. Zbl 1478.65078
Ainsworth, Mark; Fu, Guosheng
1
2019
Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276
Ainsworth, Mark; Glusa, Christian
44
2018
Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148
Ainsworth, Mark; Glusa, Christian
29
2018
Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275
Ainsworth, Mark; Fu, Guosheng
10
2018
Bernstein-Bézier bases for tetrahedral finite elements. Zbl 1440.65168
Ainsworth, Mark; Fu, Guosheng
5
2018
Multilevel techniques for compression and reduction of scientific data – the univariate case. Zbl 07704545
Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott
1
2018
Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124
Ainsworth, Mark; Mao, Zhiping
96
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
53
2017
Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219
Ainsworth, Mark; Mao, Zhiping
28
2017
Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081
Ainsworth, Mark; Glusa, Christian
6
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
3
2017
A lowest-order composite finite element exact sequence on pyramids. Zbl 1439.74381
Ainsworth, Mark; Fu, Guosheng
3
2017
Computable error bounds for finite element approximation on nonpolygonal domains. Zbl 1433.65273
Ainsworth, Mark; Rankin, Richard
1
2017
Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139
Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L.
13
2016
Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428
Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier
10
2016
Computing the Bézier control points of the Lagrangian interpolant in arbitrary dimension. Zbl 1339.65023
Ainsworth, Mark; Sánchez, Manuel A.
3
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.
74
2015
Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012
Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em
47
2015
A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
12
2015
Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas
6
2015
Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433
Ainsworth, Mark
15
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
13
2014
Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102
Ainsworth, Mark
10
2014
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
19
2013
On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard
9
2013
Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232
Ainsworth, Mark; Rankin, Richard
19
2012
Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135
Ainsworth, Mark; Ma, Xinhui
13
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
6
2012
Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120
Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
58
2011
Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194
Ainsworth, Mark; Vejchodský, Tomáš
17
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
6
2011
Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129
Ainsworth, Mark; Wajid, Hafiz Abdul
41
2010
A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144
Ainsworth, Mark
20
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
15
2010
Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050
Ainsworth, Mark; Rankin, Richard
8
2010
Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137
Ainsworth, Mark; Wajid, Hafiz Abdul
41
2009
Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019
Ainsworth, Mark; Demkowicz, Leszek
14
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
20
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
68
2007
A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353
Ainsworth, Mark
40
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
15
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.
86
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
73
2005
Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041
Dörfler, W.; Ainsworth, M.
29
2005
A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106
Ainsworth, Mark
18
2005
A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141
Ainsworth, Mark
6
2005
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103
Ainsworth, Mark
124
2004
Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112
Ainsworth, Mark
104
2004
Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022
Ainsworth, Mark
19
2004
Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088
Ainsworth, Mark; Coyle, Joe
52
2003
Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132
Ainsworth, Mark; McLean, William
15
2003
Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014
Ainsworth, Mark; Coyle, Joe
12
2003
Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017
12
2003
Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009
Ainsworth, M.; Coyle, J.
7
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
16
2002
A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041
Ainsworth, Mark; Coggins, Patrick
14
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
6
2002
Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031
Ainsworth, Mark; Coyle, Joe
30
2001
Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128
Ainsworth, Mark
24
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
Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096
Ainsworth, M.; Dörfler, 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
882
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
21
2000
The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039
Ainsworth, Mark; Coggins, Patrick
20
2000
Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091
Ainsworth, Mark; Kay, David
16
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
Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050
Sherwin, Spencer J.; Ainsworth, Mark
3
2000
...and 34 more Documents
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Cited by 3,369 Authors

73 Ainsworth, Mark
39 Vohralík, Martin
35 Carstensen, Carsten
35 Oden, John Tinsley
32 Demkowicz, Leszek F.
27 Praetorius, Dirk
27 Zhang, Zhimin
26 Díez, Pedro
23 Melenk, Jens Markus
23 Nicaise, Serge
22 Baccouch, Mahboub
22 Huang, Yunqing
21 Karniadakis, George Em
21 Li, Jichun
19 Babuška, Ivo
19 Repin, Sergeĭ Igorevich
19 Wang, Hong
17 Huerta, Antonio
17 Otárola, Enrique
16 Heuer, Norbert
15 Ern, Alexandre
15 Nochetto, Ricardo Horacio
15 Parés, Núria
15 Picasso, Marco
14 Calo, Victor Manuel
14 Führer, Thomas
14 Schöberl, Joachim
14 Schroder, Andreas
14 Zayernouri, Mohsen
14 Zhang, Shun
13 Bespalov, Alexei
13 Cai, Zhiqiang
13 D’Elia, Marta
13 Gudi, Thirupathi
13 Hauke, Guillermo
13 Hoppe, Ronald H. W.
13 Karkulik, Michael
13 Ladevèze, Pierre
13 Sauter, Stefan
13 Yang, Yidu
12 Chamoin, Ludovic
12 Chan, Jesse
12 Georgoulis, Emmanuil H.
12 Liu, Steve Wenbin
12 Merdon, Christian
12 Rankin, Richard
12 Schwab, Christoph
12 Tavener, Simon J.
12 Wu, Haijun
11 Allendes, Alejandro
11 Borthagaray, Juan Pablo
11 Chaudhry, Jehanzeb Hameed
11 Deng, Quanling
11 Estep, Donald J.
11 Gatica, Gabriel N.
11 Guo, Hailong
11 Idesman, Alexander V.
11 Stein, Erwin
11 Strouboulis, Theofanis
11 Wheeler, Mary Fanett
11 Zheng, Xiangcheng
10 Adjerid, Slimane
10 Bordas, Stéphane Pierre Alain
10 Devloo, Philippe Remy Bernard
10 Houston, Paul
10 Hu, Jun
10 Mei, Liquan
10 Pardo, David
10 Park, Eun-Jae
10 Patera, Anthony T.
10 Prudhomme, Serge
10 Rank, Ernst
10 van der Vegt, Jaap J. W.
10 Wick, Thomas
10 Wohlmuth, Barbara I.
10 Zou, Qingsong
9 Antil, Harbir
9 Bertrand, Fleurianne
9 Chaumont-Frelet, Théophile
9 Chen, Yanping
9 Creusé, Emmanuel
9 Du, Yu
9 Düster, Alexander
9 Feischl, Michael
9 Gopalakrishnan, Jay
9 Jiang, Xiaoyun
9 Kim, Kwang Yeon
9 Mao, Zhiping
9 Rachowicz, Waldemar
9 Ródenas, Juan José
9 Stephan, Ernst Peter
9 Xu, Yifeng
9 Yan, Ningning
8 Beirão da Veiga, Lourenço
8 Bi, Hai
8 Carey, Graham Francis
8 Du, Shaohong
8 Ervin, Vincent J.
8 Fu, Guosheng
8 Glusa, Christian
...and 3,269 more Authors
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Cited in 225 Serials

459 Computer Methods in Applied Mechanics and Engineering
172 Journal of Scientific Computing
171 Computers & Mathematics with Applications
170 Journal of Computational Physics
120 Journal of Computational and Applied Mathematics
108 Numerische Mathematik
96 Applied Numerical Mathematics
93 International Journal for Numerical Methods in Engineering
86 SIAM Journal on Scientific Computing
83 Mathematics of Computation
81 SIAM Journal on Numerical Analysis
54 Computational Mechanics
54 Numerical Methods for Partial Differential Equations
48 Applied Mathematics and Computation
45 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
31 Computational Methods in Applied Mathematics
26 Advances in Computational Mathematics
24 Computers and Fluids
22 Mathematics and Computers in Simulation
22 Engineering Analysis with Boundary Elements
21 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
19 Fractional Calculus & Applied Analysis
19 Journal of Numerical Mathematics
17 Calcolo
16 Applied Mathematical Modelling
16 Communications in Computational Physics
15 International Journal of Computer Mathematics
14 International Journal for Numerical Methods in Fluids
14 BIT
14 Applied Mathematics Letters
14 Communications in Nonlinear Science and Numerical Simulation
13 Numerical Algorithms
13 Computational and Applied Mathematics
12 Communications in Numerical Methods in Engineering
11 Applications of Mathematics
11 International Journal of Numerical Analysis and Modeling
11 Communications on Applied Mathematics and Computation
10 Journal of Mathematical Sciences (New York)
10 Archives of Computational Methods in Engineering
10 Science China. Mathematics
8 Mathematical Methods in the Applied Sciences
8 Numerical Linear Algebra with Applications
8 Computing and Visualization in Science
8 Computational Geosciences
8 Foundations of Computational Mathematics
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
8 Numerical Mathematics: Theory, Methods and Applications
7 COMPEL
7 Discrete and Continuous Dynamical Systems. Series B
7 Advances in Applied Mathematics and Mechanics
6 Computing
6 International Journal of Computational Fluid Dynamics
6 International Journal of Computational Methods
6 Acta Numerica
6 East Asian Journal on Applied Mathematics
6 SIAM/ASA Journal on Uncertainty Quantification
5 Computer Physics Communications
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5 Computational Mathematics and Mathematical Physics
5 SIAM Journal on Mathematical Analysis
5 SIAM Review
5 Mathematical Problems in Engineering
5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
4 Applicable Analysis
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4 SIAM Journal on Control and Optimization
4 Physica D
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4 European Journal of Mechanics. A. Solids
4 Engineering Computations
4 Lobachevskii Journal of Mathematics
4 Central European Journal of Mathematics
4 Advances in Difference Equations
4 GAMM-Mitteilungen
4 Frontiers of Mathematics in China
4 Discrete and Continuous Dynamical Systems. Series S
3 Journal of Mathematical Physics
3 Wave Motion
3 ACM Transactions on Mathematical Software
3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
3 Applied Mathematics and Mechanics. (English Edition)
3 Computer Aided Geometric Design
3 Constructive Approximation
3 Science in China. Series A
3 Archive of Applied Mechanics
3 Journal of Nonlinear Science
3 Computational Optimization and Applications
3 ETNA. Electronic Transactions on Numerical Analysis
3 Journal of Inequalities and Applications
3 Journal of Applied Mathematics
3 Journal of Physics A: Mathematical and Theoretical
3 Advances in Numerical Analysis
3 AIMS Mathematics
3 SMAI Journal of Computational Mathematics
3 Electronic Research Archive
2 Inverse Problems
2 Chaos, Solitons and Fractals
2 Journal of Differential Equations
...and 125 more Serials
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Cited in 44 Fields

2,321 Numerical analysis (65-XX)
1,157 Partial differential equations (35-XX)
511 Fluid mechanics (76-XX)
508 Mechanics of deformable solids (74-XX)
170 Optics, electromagnetic theory (78-XX)
140 Calculus of variations and optimal control; optimization (49-XX)
125 Real functions (26-XX)
70 Ordinary differential equations (34-XX)
66 Approximations and expansions (41-XX)
49 Probability theory and stochastic processes (60-XX)
41 Computer science (68-XX)
32 Operator theory (47-XX)
32 Statistical mechanics, structure of matter (82-XX)
30 Integral equations (45-XX)
28 Special functions (33-XX)
28 Geophysics (86-XX)
27 Biology and other natural sciences (92-XX)
25 Classical thermodynamics, heat transfer (80-XX)
22 Functional analysis (46-XX)
21 Linear and multilinear algebra; matrix theory (15-XX)
19 Global analysis, analysis on manifolds (58-XX)
17 Statistics (62-XX)
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14 Operations research, mathematical programming (90-XX)
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9 Information and communication theory, circuits (94-XX)
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