Edit Profile (opens in new tab) Ainsworth, Mark Compute Distance To: Compute Author ID: ainsworth.mark Published as: Ainsworth, Mark; Ainsworth, M. External Links: MGP Documents Indexed: 137 Publications since 1989, including 1 Book 5 Contributions as Editor Co-Authors: 66 Co-Authors with 118 Joint Publications 2,032 Co-Co-Authors all top 5 Co-Authors 20 single-authored 12 Oden, John Tinsley 11 Rankin, Richard 8 Glusa, Christian 6 Parker, Charles 5 Mao, Zhiping 5 Mihai, L. Angela 5 Senior, Bill 4 Barrenechea, Gabriel R. 4 Davydov, Oleg V. 4 Fu, Guosheng 4 Jiang, Shuai 4 Klasky, Scott 4 Vejchodský, Tomáš 4 Whitney, Ben 3 Allendes, Alejandro 3 Coggins, Patrick 3 Coyle, Joe 3 Craig, Alan W. 3 Demkowicz, Leszek F. 3 Dorfler, Willy 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 Dong, Justin 2 Guo, Benqi 2 Light, William A. 2 Pinchedez, Katia 2 Sánchez, Manuel A. 2 Sherwin, Spencer J. 2 Shin, Yeonjong 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 25 Computer Methods in Applied Mechanics and Engineering 22 SIAM Journal on Numerical Analysis 19 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 all top 5 Fields 120 Numerical analysis (65-XX) 60 Partial differential equations (35-XX) 27 Fluid mechanics (76-XX) 22 Mechanics of deformable solids (74-XX) 9 Computer science (68-XX) 5 General and overarching topics; collections (00-XX) 5 Optics, electromagnetic theory (78-XX) 3 Operations research, mathematical programming (90-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 Dynamical systems and ergodic theory (37-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 127 Publications have been cited 3,310 times in 2,299 Documents Cited by ▼ Year ▼ A posteriori error estimation in finite element analysis. Zbl 1008.65076Ainsworth, Mark; Oden, J. Tinsley 738 2000 A posteriori error estimation in finite element analysis. Zbl 0895.76040Ainsworth, Mark; Oden, J. Tinsley 241 1997 A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080Ainsworth, Mark; Oden, J. Tinsley 169 1993 Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103Ainsworth, Mark 116 2004 Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112Ainsworth, Mark 92 2004 Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. Zbl 1102.76032Ainsworth, M.; Monk, P.; Muniz, W. 79 2006 What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em 72 2020 Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124Ainsworth, Mark; Mao, Zhiping 69 2017 A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em. 66 2015 Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102Ainsworth, Mark 65 2005 A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083Ainsworth, Mark 59 2007 A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067Ainsworth, Mark; Oden, J. Tinsley 56 1997 Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057Ainsworth, Mark; Senior, Bill 54 1997 Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 49 2011 A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods. Zbl 0778.73060Ainsworth, Mark; Oden, J. Tinsley 49 1992 An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Zbl 0844.76056Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark 47 1994 Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114Ainsworth, Mark; Babuska, Ivo 45 1998 Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088Ainsworth, Mark; Coyle, Joe 43 2003 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 42 2015 A posteriori error estimators for second order elliptic systems. II: An optimal order process for calculating self-equilibrating fluxes. Zbl 0789.65083Ainsworth, M.; Oden, J. T. 41 1993 A preconditioner based on domain decomposition for \(h\)-\(p\) finite-element approximation on quasi-uniform meshes. Zbl 0855.65044Ainsworth, Mark 39 1996 The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125Ainsworth, Mark; McLean, William; Tran, Thanh 38 1999 A posteriori error estimators in the finite element method. Zbl 0757.65109Ainsworth, Mark; Craig, Alan 36 1992 An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052Ainsworth, Mark; Senior, Bill 36 1998 Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137Ainsworth, Mark; Wajid, Hafiz Abdul 34 2009 Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129Ainsworth, Mark; Wajid, Hafiz Abdul 34 2010 A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353Ainsworth, Mark 34 2007 Analysis of the Zienkiewicz-Zhu a-posteriori error estimator in the finite element method. Zbl 0716.73082Ainsworth, M.; Zhu, J. Z.; Craig, A. W.; Zienkiewicz, O. C. 30 1989 Local a posteriori error estimators for variational inequalities. Zbl 0768.65032Ainsworth, Mark; Oden, J. Tinsley; Lee, C. Y. 28 1993 Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031Ainsworth, Mark; Coyle, Joe 28 2001 Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041Dörfler, W.; Ainsworth, M. 27 2005 Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276Ainsworth, Mark; Glusa, Christian 25 2018 The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122Ainsworth, Mark; Kay, David 24 1999 Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148Ainsworth, Mark; Glusa, Christian 23 2018 Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219Ainsworth, Mark; Mao, Zhiping 22 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 1439.65142Ainsworth, Mark; Glusa, Christian 21 2017 Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128Ainsworth, Mark 20 2001 Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141Ainsworth, Mark; Rankin, Richard 19 2008 The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039Ainsworth, Mark; Coggins, Patrick 19 2000 An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084Ainsworth, Mark; Guo, Benqi 19 2000 Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations. Zbl 0934.76040Ainsworth, Mark; Sherwin, Spencer 18 1999 A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144Ainsworth, Mark 17 2010 Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091Ainsworth, Mark; Kay, David 16 2000 A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106Ainsworth, Mark 15 2005 A posteriori error estimators for second order elliptic systems. I: Theoretical foundations and a posteriori error analysis. Zbl 0764.65060Ainsworth, Mark; Oden, J. Tinsley 15 1993 Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232Ainsworth, Mark; Rankin, Richard 15 2012 \(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119Ainsworth, Mark; Pinchedez, Katia 15 2002 Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022Ainsworth, Mark 15 2004 Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433Ainsworth, Mark 15 2014 Solution of elastic scattering problems in linear acoustics using \(h\)-\(p\) boundary element methods. Zbl 0770.73092Demkowicz, L.; Oden, J. Tinsley; Ainsworth, M.; Geng, P. 14 1991 Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194Ainsworth, Mark; Vejchodský, Tomáš 14 2011 Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. Zbl 1173.76424Ainsworth, Mark; Demkowicz, Leszek; Kim, Chang-Wan 14 2007 A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041Ainsworth, Mark; Coggins, Patrick 14 2002 Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019Ainsworth, Mark; Demkowicz, Leszek 13 2009 Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. Zbl 1208.65155Ainsworth, Mark; Rankin, Richard 12 2010 A posteriori error estimation for \(h-p\) approximations in elastostatics. Zbl 0802.73072Ainsworth, M.; Oden, J. T.; Wu, W. 12 1994 Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132Ainsworth, Mark; McLean, William 12 2003 Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014Ainsworth, Mark; Coyle, Joe 12 2003 A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. Zbl 0860.65111Ainsworth, Mark 11 1996 Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L. 11 2016 A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 10 2015 Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168Ainsworth, Mark; Jiang, Shuai 10 2019 Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. Zbl 1208.65156Ainsworth, Mark; Rankin, Richard 9 2011 Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135Ainsworth, Mark; Ma, Xinhui 9 2012 A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Zbl 0912.65087Ainsworth, Mark 9 1998 The influence and selection of subspaces for a posteriori error estimators. Zbl 0873.65099Ainsworth, Mark 8 1996 Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096Ainsworth, M.; Dörfler, W. 8 2001 Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier 8 2016 A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem. Zbl 0999.65116Ainsworth, Mark; Kelly, Donald W. 8 2001 An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing. Zbl 1441.65089Ainsworth, Mark; Jiang, Shuai; Sanchéz, Manuel A. 8 2019 \(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113Ainsworth, Mark; Senior, Bill 7 1999 Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215Ainsworth, Mark; Rankin, Richard 7 2008 Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050Ainsworth, Mark; Rankin, Richard 7 2010 Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. Zbl 1049.65135Ainsworth, Mark; Arnold, Mark 7 2000 On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 7 2013 Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Zbl 1425.65140Ainsworth, Mark; Vejchodský, Tomáš 7 2014 Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Zbl 1022.65131Ainsworth, Mark; Guo, Benqi 7 2002 A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090Ainsworth, Mark; Vejchodský, Tomáš 7 2019 Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102Ainsworth, Mark 7 2014 Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275Ainsworth, Mark; Fu, Guosheng 7 2018 Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009Ainsworth, M.; Coyle, J. 6 2003 Three-step \(h\)-\(p\) adaptive strategy for the incompressible Navier-Stokes equations. Zbl 0844.76057Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark 5 1995 A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141Ainsworth, Mark 5 2005 Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055Ainsworth, Mark; Arnold, Mark 5 2001 Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076Ainsworth, Mark; Rankin, Richard 5 2011 Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. Zbl 1333.76050Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 5 2012 Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081Ainsworth, Mark; Glusa, Christian 5 2017 The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076Ainsworth, Mark; Pinchedez, Katia 5 2002 Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas 5 2015 Preconditioning the mass matrix for high order finite element approximation on tetrahedra. Zbl 1466.65174Ainsworth, Mark; Jiang, Shuai 4 2021 Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem. Zbl 0890.65109Ainsworth, M.; Kelly, D. W.; Sloan, I. H.; Wang, S. L. 4 1997 A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355Ainsworth, Mark; Mihai, L. Angela 4 2006 Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. Zbl 1455.65207Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 4 2013 Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott 4 2019 \(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020Ainsworth, Mark; Parker, Charles 4 2020 Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043Ainsworth, Mark 3 1999 Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041Ainsworth, Mark; Glusa, Christian 3 2017 Simple and practical error estimation and adaptivity: h and h-p version procedures. Zbl 0693.73047Zienkiewicz, O. C.; Zhu, J. Z.; Craig, A. W.; Ainsworth, M. 3 1989 Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050Sherwin, Spencer J.; Ainsworth, Mark 3 2000 Modeling and numerical analysis of masonry structures. Zbl 1115.74036Ainsworth, Mark; Mihai, L. Angela 3 2007 Preconditioning the mass matrix for high order finite element approximation on tetrahedra. Zbl 1466.65174Ainsworth, Mark; Jiang, Shuai 4 2021 Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. I: Uniform stability. Zbl 1465.76049Ainsworth, Mark; Parker, Charles 2 2021 Mass conserving mixed \(hp\)-FEM approximations to Stokes flow. II: Optimal convergence. Zbl 1465.76050Ainsworth, Mark; Parker, Charles 2 2021 Preconditioning high order \(H^2\) conforming finite elements on triangles. Zbl 1472.65138Ainsworth, Mark; Parker, Charles 2 2021 Plateau phenomenon in gradient descent training of RELU networks: explanation, quantification, and avoidance. Zbl 1487.65070Ainsworth, Mark; Shin, Yeonjong 1 2021 Galerkin neural networks: a framework for approximating variational equations with error control. Zbl 1486.65238Ainsworth, Mark; Dong, Justin 1 2021 What is the fractional Laplacian? A comparative review with new results. Zbl 1453.35179Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em 72 2020 \(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020Ainsworth, Mark; Parker, Charles 4 2020 Fractional phase-field crystal modelling: analysis, approximation and pattern formation. Zbl 1443.74160Ainsworth, Mark; Mao, Zhiping 3 2020 Some remarks on spectral convergence and stability of iso-geometric analysis. Zbl 07337902Ainsworth, Mark; Davydov, Oleg; Wang, Hongrui 2 2020 Preconditioning the mass matrix for high order finite element approximation on triangles. Zbl 1426.65168Ainsworth, Mark; Jiang, Shuai 10 2019 An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing. Zbl 1441.65089Ainsworth, Mark; Jiang, Shuai; Sanchéz, Manuel A. 8 2019 A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090Ainsworth, Mark; Vejchodský, Tomáš 7 2019 Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott 4 2019 High-order composite finite element exact sequences based on tetrahedral-hexahedral-prismatic-pyramidal partitions. Zbl 1441.65096Devloo, Philippe R. B.; Durán, Omar; Gomes, Sônia M.; Ainsworth, Mark 2 2019 Dispersive behavior of an energy-conserving discontinuous Galerkin method for the one-way wave equation. Zbl 1478.65078Ainsworth, Mark; Fu, Guosheng 1 2019 Multilevel techniques for compression and reduction of scientific data-quantitative control of accuracy in derived quantities. Zbl 1429.68069Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott 1 2019 Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276Ainsworth, Mark; Glusa, Christian 25 2018 Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148Ainsworth, Mark; Glusa, Christian 23 2018 Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275Ainsworth, Mark; Fu, Guosheng 7 2018 Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124Ainsworth, Mark; Mao, Zhiping 69 2017 Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219Ainsworth, Mark; Mao, Zhiping 22 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 1439.65142Ainsworth, Mark; Glusa, Christian 21 2017 Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081Ainsworth, Mark; Glusa, Christian 5 2017 Is the multigrid method fault tolerant? The multilevel case. Zbl 1377.65041Ainsworth, Mark; Glusa, Christian 3 2017 Compression using lossless decimation: analysis and application. Zbl 1420.68085Ainsworth, Mark; Klasky, Scott; Whitney, Ben 2 2017 A lowest-order composite finite element exact sequence on pyramids. Zbl 1439.74381Ainsworth, Mark; Fu, Guosheng 1 2017 Computable error bounds for finite element approximation on nonpolygonal domains. Zbl 1433.65273Ainsworth, Mark; Rankin, Richard 1 2017 Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L. 11 2016 Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier 8 2016 Computing the Bézier control points of the Lagrangian interpolant in arbitrary dimension. Zbl 1339.65023Ainsworth, Mark; Sánchez, Manuel A. 2 2016 Multigrid at scale? Zbl 1352.65622Ainsworth, Mark; Glusa, Christian 1 2016 A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em. 66 2015 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 42 2015 A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 10 2015 Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas 5 2015 Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433Ainsworth, Mark 15 2014 Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Zbl 1425.65140Ainsworth, Mark; Vejchodský, Tomáš 7 2014 Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102Ainsworth, Mark 7 2014 On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 7 2013 Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. Zbl 1455.65207Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 4 2013 Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232Ainsworth, Mark; Rankin, Richard 15 2012 Non-uniform order mixed FEM approximation: implementation, post-processing, computable error bound and adaptivity. Zbl 1243.65135Ainsworth, Mark; Ma, Xinhui 9 2012 Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem. Zbl 1333.76050Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 5 2012 Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 49 2011 Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194Ainsworth, Mark; Vejchodský, Tomáš 14 2011 Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. Zbl 1208.65156Ainsworth, Mark; Rankin, Richard 9 2011 Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076Ainsworth, Mark; Rankin, Richard 5 2011 Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129Ainsworth, Mark; Wajid, Hafiz Abdul 34 2010 A framework for obtaining guaranteed error bounds for finite element approximations. Zbl 1191.65144Ainsworth, 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 1208.65155Ainsworth, Mark; Rankin, Richard 12 2010 Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050Ainsworth, Mark; Rankin, Richard 7 2010 Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137Ainsworth, Mark; Wajid, Hafiz Abdul 34 2009 Explicit polynomial preserving trace liftings on a triangle. Zbl 1175.46019Ainsworth, Mark; Demkowicz, Leszek 13 2009 A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Zbl 1231.74429Mihai, L. Angela; Ainsworth, Mark 3 2009 An adaptive multi-scale computational modelling of Clare College Bridge. Zbl 1227.74033Mihai, L. A.; Ainsworth, Mark 2 2009 An adaptive multi-scale approach to the modelling of masonry structures. Zbl 1183.74179Ainsworth, Mark; Mihai, L. Angela 1 2009 Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141Ainsworth, Mark; Rankin, Richard 19 2008 Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215Ainsworth, Mark; Rankin, Richard 7 2008 A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083Ainsworth, Mark 59 2007 A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353Ainsworth, Mark 34 2007 Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. Zbl 1173.76424Ainsworth, Mark; Demkowicz, Leszek; Kim, Chang-Wan 14 2007 Modeling and numerical analysis of masonry structures. Zbl 1115.74036Ainsworth, Mark; Mihai, L. Angela 3 2007 Dispersive and dissipative properties of discontinuous Galerkin finite element methods for the second-order wave equation. Zbl 1102.76032Ainsworth, M.; Monk, P.; Muniz, W. 79 2006 A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355Ainsworth, Mark; Mihai, L. Angela 4 2006 Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102Ainsworth, Mark 65 2005 Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041Dörfler, W.; Ainsworth, M. 27 2005 A synthesis of a posteriori error estimation techniques for conforming, non-conforming and discontinuous Galerkin finite element methods. Zbl 1098.65106Ainsworth, Mark 15 2005 A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141Ainsworth, Mark 5 2005 Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103Ainsworth, Mark 116 2004 Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112Ainsworth, Mark 92 2004 Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022Ainsworth, Mark 15 2004 Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088Ainsworth, Mark; Coyle, Joe 43 2003 Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132Ainsworth, Mark; McLean, William 12 2003 Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014Ainsworth, Mark; Coyle, Joe 12 2003 Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009Ainsworth, M.; Coyle, J. 6 2003 Topics in computational wave propagation. Direct and inverse problems. Zbl 1018.00017 3 2003 Dispersive properties of high-order finite elements. Zbl 1047.76039Ainsworth, Mark 1 2003 \(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119Ainsworth, Mark; Pinchedez, Katia 15 2002 A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041Ainsworth, Mark; Coggins, Patrick 14 2002 Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Zbl 1022.65131Ainsworth, Mark; Guo, Benqi 7 2002 The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076Ainsworth, Mark; Pinchedez, Katia 5 2002 Hierachic \(hp\)-edge element families for Maxwell’s equations on hybrid quadrilateral/triangular meshes. Zbl 0991.78031Ainsworth, Mark; Coyle, Joe 28 2001 Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128Ainsworth, Mark 20 2001 Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. Zbl 0988.65096Ainsworth, M.; Dörfler, W. 8 2001 A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem. Zbl 0999.65116Ainsworth, Mark; Kelly, Donald W. 8 2001 Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055Ainsworth, Mark; Arnold, Mark 5 2001 A posteriori error estimation in finite element analysis. Zbl 1008.65076Ainsworth, Mark; Oden, J. Tinsley 738 2000 The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039Ainsworth, Mark; Coggins, Patrick 19 2000 An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084Ainsworth, Mark; Guo, Benqi 19 2000 Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091Ainsworth, Mark; Kay, David 16 2000 Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. Zbl 1049.65135Ainsworth, Mark; Arnold, Mark 7 2000 Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050Sherwin, Spencer J.; Ainsworth, Mark 3 2000 Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092Ainsworth, Mark; McLean, Bill; Tran, Thanh 3 2000 Mixed \(hp\)-finite element methods for incompressible flow. Zbl 0981.76051Ainsworth, M.; Coggins, P.; Senior, B. 1 2000 Some useful techniques for pointwise and local error estimates of the quantities of interest in the finite element approximation. Zbl 0977.65093Cao, T.; Kelly, D. W.; Ainsworth, M. 1 2000 The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125Ainsworth, Mark; McLean, William; Tran, Thanh 38 1999 The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122Ainsworth, Mark; Kay, David 24 1999 Domain decomposition preconditioners for \(p\) and \(hp\) finite element approximation of Stokes equations. Zbl 0934.76040Ainsworth, Mark; Sherwin, Spencer 18 1999 \(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113Ainsworth, Mark; Senior, Bill 7 1999 ...and 27 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,875 Authors 70 Ainsworth, Mark 33 Oden, John Tinsley 33 Vohralík, Martin 32 Carstensen, Carsten 31 Demkowicz, Leszek F. 26 Zhang, Zhimin 24 Díez, Pedro 24 Praetorius, Dirk 21 Nicaise, Serge 19 Baccouch, Mahboub 18 Huang, Yunqing 18 Repin, Sergeĭ Igorevich 17 Babuška, Ivo 17 Karniadakis, George Em 17 Li, Jichun 16 Otárola, Enrique 16 Wang, Hong 15 Heuer, Norbert 15 Huerta, Antonio 13 Ern, Alexandre 13 Gudi, Thirupathi 13 Ladevèze, Pierre 13 Melenk, Jens Markus 13 Parés, Núria 13 Schöberl, Joachim 12 Calo, Victor Manuel 12 Führer, Thomas 12 Karkulik, Michael 12 Liu, Steve Wenbin 12 Picasso, Marco 12 Sauter, Stefan A. 12 Zayernouri, Mohsen 11 Allendes, Alejandro 11 Bespalov, Alexei 11 Chan, Jesse 11 Gatica, Gabriel N. 11 Hoppe, Ronald H. W. 11 Nochetto, Ricardo Horacio 11 Schroder, Andreas 11 Strouboulis, Theofanis 11 Yang, Yidu 11 Zhang, Shun 10 Bordas, Stéphane Pierre Alain 10 Guo, Hailong 10 Hauke, Guillermo 10 Houston, Paul 10 Merdon, Christian 10 Patera, Anthony T. 10 Rankin, Richard 10 Stein, Erwin 10 Tavener, Simon J. 10 van der Vegt, Jaap J. W. 9 Adjerid, Slimane 9 Cai, Zhiqiang 9 Chaudhry, Jehanzeb Hameed 9 Deng, Quanling 9 Düster, Alexander 9 Estep, Donald J. 9 Feischl, Michael 9 Georgoulis, Emmanuil H. 9 Kim, Kwang Yeon 9 Pardo, David 9 Rank, Ernst 9 Ródenas, Juan José 9 Schwab, Christoph 9 Wheeler, Mary Fanett 9 Wick, Thomas 9 Wu, Haijun 9 Yan, Ningning 9 Zheng, Xiangcheng 8 Carey, Graham Francis 8 Chamoin, Ludovic 8 Chen, Yanping 8 Creusé, Emmanuel 8 D’Elia, Marta 8 Du, Yu 8 Ervin, Vincent J. 8 Fu, Guosheng 8 Glusa, Christian 8 Park, Eun-Jae 8 Prudhomme, Serge 8 Rachowicz, Waldemar 8 Shephard, Mark S. 8 Stenberg, Rolf 8 Veeser, Andreas 8 Wohlmuth, Barbara I. 8 Xu, Yifeng 8 Zhou, Jianwei 8 Zou, Qingsong 7 Abdulle, Assyr 7 Antil, Harbir 7 Beirão da Veiga, Lourenço 7 Beuchler, Sven 7 Bi, Hai 7 Borthagaray, Juan Pablo 7 Du, Shaohong 7 Fuenmayor, Francisco Javier 7 Giani, Stefano 7 Hiptmair, Ralf 7 Idesman, Alexander V. ...and 2,775 more Authors all top 5 Cited in 196 Serials 390 Computer Methods in Applied Mechanics and Engineering 146 Journal of Computational Physics 145 Computers & Mathematics with Applications 142 Journal of Scientific Computing 104 Journal of Computational and Applied Mathematics 97 Numerische Mathematik 90 Applied Numerical Mathematics 83 International Journal for Numerical Methods in Engineering 78 Mathematics of Computation 75 SIAM Journal on Scientific Computing 69 SIAM Journal on Numerical Analysis 50 Computational Mechanics 41 Applied Mathematics and Computation 41 Numerical Methods for Partial Differential Equations 38 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 23 Computers and Fluids 23 Computational Methods in Applied Mathematics 22 Engineering Analysis with Boundary Elements 21 Advances in Computational Mathematics 20 M\(^3\)AS. 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Solids 4 Engineering Computations 4 Advances in Difference Equations 4 Frontiers of Mathematics in China 4 East Asian Journal on Applied Mathematics 3 Applicable Analysis 3 Journal of Fluid Mechanics 3 Journal of Mathematical Physics 3 Wave Motion 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 ETNA. Electronic Transactions on Numerical Analysis 3 Computing and Visualization in Science 3 Lobachevskii Journal of Mathematics 3 Journal of Applied Mathematics 3 Central European Journal of Mathematics 3 Discrete and Continuous Dynamical Systems. Series S 3 Advances in Numerical Analysis 3 AIMS Mathematics 3 Electronic Research Archive 2 ACM Transactions on Mathematical Software 2 Journal of Differential Equations 2 Kybernetika 2 Nonlinear Analysis. Theory, Methods & Applications. 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Terceira Série ...and 96 more Serials all top 5 Cited in 42 Fields 1,954 Numerical analysis (65-XX) 947 Partial differential equations (35-XX) 436 Fluid mechanics (76-XX) 434 Mechanics of deformable solids (74-XX) 144 Optics, electromagnetic theory (78-XX) 118 Calculus of variations and optimal control; optimization (49-XX) 86 Real functions (26-XX) 60 Ordinary differential equations (34-XX) 45 Approximations and expansions (41-XX) 31 Probability theory and stochastic processes (60-XX) 26 Geophysics (86-XX) 25 Operator theory (47-XX) 24 Computer science (68-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Classical thermodynamics, heat transfer (80-XX) 21 Integral equations (45-XX) 20 Biology and other natural sciences (92-XX) 19 Special functions (33-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 16 Functional analysis (46-XX) 15 Global analysis, analysis on manifolds (58-XX) 13 Statistics (62-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 9 Operations research, mathematical programming (90-XX) 8 Systems theory; control (93-XX) 7 Potential theory (31-XX) 6 Quantum theory (81-XX) 6 Information and communication theory, circuits (94-XX) 5 Mechanics of particles and systems (70-XX) 4 General and overarching topics; collections (00-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Difference and functional equations (39-XX) 3 Integral transforms, operational calculus (44-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Relativity and gravitational theory (83-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year