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: 135 Publications since 1989, including 1 Book 5 Contributions as Editor Co-Authors: 66 Co-Authors with 116 Joint Publications 1,971 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 Guo, Benqi 2 Light, William A. 2 Pinchedez, Katia 2 Sánchez, Manuel A. 2 Sherwin, Spencer J. 2 Sloan, Ian Hugh 2 Wajid, Hafiz Abdul 2 Zayernouri, Mohsen 2 Zienkiewicz, Olgierd Cecil 1 Andrews, Derek J. 1 Babuška, Ivo 1 Cai, Wei 1 Carstensen, Carsten 1 Davies, Penny J. 1 Devloo, Philippe Remy Bernard 1 Dong, Justin 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 Shin, Yeonjong 1 Song, Fangying 1 Wachtel, Andreas 1 Wang, Hongrui 1 Zheng, Xiaoning all top 5 Serials 24 Computer Methods in Applied Mechanics and Engineering 22 SIAM Journal on Numerical Analysis 18 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 119 Numerical analysis (65-XX) 60 Partial differential equations (35-XX) 27 Fluid mechanics (76-XX) 20 Mechanics of deformable solids (74-XX) 7 Computer science (68-XX) 5 General and overarching topics; collections (00-XX) 5 Optics, electromagnetic theory (78-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 Operations research, mathematical programming (90-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 123 Publications have been cited 3,172 times in 2,216 Documents Cited by ▼ Year ▼ A posteriori error estimation in finite element analysis. Zbl 1008.65076Ainsworth, Mark; Oden, J. Tinsley 722 2000 A posteriori error estimation in finite element analysis. Zbl 0895.76040Ainsworth, Mark; Oden, J. Tinsley 235 1997 A unified approach to a posteriori error estimation using element residual methods. Zbl 0797.65080Ainsworth, Mark; Oden, J. Tinsley 166 1993 Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Zbl 1058.65103Ainsworth, Mark 108 2004 Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112Ainsworth, Mark 86 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. 76 2006 Robust a posteriori error estimation for nonconforming finite element approximation. Zbl 1085.65102Ainsworth, Mark 62 2005 Analysis and approximation of a fractional Cahn-Hilliard equation. Zbl 1369.65124Ainsworth, Mark; Mao, Zhiping 62 2017 A unified Petrov-Galerkin spectral method for fractional PDEs. Zbl 1425.65127Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em. 59 2015 A posteriori error estimation for discontinuous Galerkin finite element approximation. Zbl 1151.65083Ainsworth, Mark 56 2007 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 56 2020 Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Zbl 0906.73057Ainsworth, Mark; Senior, Bill 54 1997 A posteriori error estimators for the Stokes and Oseen equations. Zbl 0879.65067Ainsworth, Mark; Oden, J. Tinsley 53 1997 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 Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 45 2011 Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114Ainsworth, Mark; Babuska, Ivo 44 1998 Hierarchic finite element bases on unstructured tetrahedral meshes. Zbl 1042.65088Ainsworth, Mark; Coyle, Joe 41 2003 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. 40 1993 A preconditioner based on domain decomposition for \(h\)-\(p\) finite-element approximation on quasi-uniform meshes. Zbl 0855.65044Ainsworth, Mark 39 1996 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 38 2015 The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. Zbl 0947.65125Ainsworth, Mark; McLean, William; Tran, Thanh 36 1999 A posteriori error estimators in the finite element method. Zbl 0757.65109Ainsworth, Mark; Craig, Alan 36 1992 A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. Zbl 1159.65353Ainsworth, Mark 34 2007 An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052Ainsworth, Mark; Senior, Bill 34 1998 Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129Ainsworth, Mark; Wajid, Hafiz Abdul 33 2010 Dispersive and dissipative behavior of the spectral element method. Zbl 1204.65137Ainsworth, Mark; Wajid, Hafiz Abdul 30 2009 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. 25 2005 Towards an efficient finite element method for the integral fractional Laplacian on polygonal domains. Zbl 1407.65276Ainsworth, Mark; Glusa, Christian 24 2018 Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219Ainsworth, Mark; Mao, Zhiping 21 2017 The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122Ainsworth, Mark; Kay, David 20 1999 Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148Ainsworth, Mark; Glusa, Christian 20 2018 The stability of mixed \(hp\)-finite element methods for Stokes flow on high aspect ratio elements. Zbl 0989.76039Ainsworth, Mark; Coggins, Patrick 19 2000 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 19 2017 Essential boundary conditions and multi-point constraints in finite element analysis. Zbl 0992.65128Ainsworth, Mark 18 2001 An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions. Zbl 0953.65084Ainsworth, Mark; Guo, Benqi 18 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 Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. Zbl 1180.65141Ainsworth, Mark; Rankin, Richard 17 2008 Approximation theory for the \(hp\)-version finite element method and application to the nonlinear Laplacian. Zbl 0972.65091Ainsworth, Mark; Kay, David 16 2000 Dispersive properties of high-order Nédélec/edge element approximation of the time-harmonic Maxwells equations. Zbl 1079.78022Ainsworth, Mark 15 2004 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 \(hp\)-approximation theory for BDFM and RT finite elements on quadrilaterals. Zbl 1035.65119Ainsworth, Mark; Pinchedez, Katia 15 2002 Dispersive behaviour of high order finite element schemes for the one-way wave equation. Zbl 1349.65433Ainsworth, Mark 15 2014 A uniformly stable family of mixed \(hp\)-finite elements with continuous pressures for incompressible flow. Zbl 1017.76041Ainsworth, Mark; Coggins, Patrick 14 2002 Guaranteed computable bounds on quantities of interest in finite element computations. Zbl 1242.65232Ainsworth, Mark; Rankin, Richard 14 2012 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 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 13 2011 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 Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Zbl 1073.65132Ainsworth, Mark; McLean, William 12 2003 A posteriori error estimation for \(h-p\) approximations in elastostatics. Zbl 0802.73072Ainsworth, M.; Oden, J. T.; Wu, W. 11 1994 Conditioning of hierarchic \(p\)-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Zbl 1091.78014Ainsworth, Mark; Coyle, Joe 11 2003 A Bernstein-Bézier basis for arbitrary order Raviart-Thomas finite elements. Zbl 1315.65096Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 10 2015 Bernstein-Bézier finite elements on tetrahedral-hexahedral-pyramidal partitions. Zbl 1425.65139Ainsworth, Mark; Davydov, Oleg; Schumaker, Larry L. 10 2016 A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. Zbl 0860.65111Ainsworth, Mark 10 1996 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 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 Discrete extension operators for mixed finite element spaces on locally refined meshes. Zbl 1416.65428Ainsworth, Mark; Guzmán, Johnny; Sayas, Francisco-Javier 8 2016 Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. Zbl 1188.74050Ainsworth, Mark; Rankin, Richard 7 2010 Robust a posteriori error estimation for the nonconforming fortin–soulie finite element approximation. Zbl 1198.65215Ainsworth, Mark; Rankin, Richard 7 2008 The influence and selection of subspaces for a posteriori error estimators. Zbl 0873.65099Ainsworth, Mark 7 1996 Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102Ainsworth, Mark 7 2014 \(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. Zbl 0941.65113Ainsworth, Mark; Senior, Bill 7 1999 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 Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations. Zbl 1407.65275Ainsworth, Mark; Fu, Guosheng 7 2018 An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing. Zbl 1441.65089Ainsworth, Mark; Jiang, Shuai; Sanchéz, Manuel A. 7 2019 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 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 6 2014 On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard 6 2013 A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090Ainsworth, Mark; Vejchodský, Tomáš 6 2019 Computation of Maxwell eigenvalues on curvilinear domains using \(hp\)-version Nédélec elements. Zbl 1055.78009Ainsworth, M.; Coyle, J. 6 2003 Computable error bounds for some simple dimensionally reduced models on thin domains. Zbl 1031.74055Ainsworth, Mark; Arnold, Mark 5 2001 Stabilization of high aspect ratio mixed finite elements for incompressible flow. Zbl 1322.76038Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas 5 2015 A posteriori error estimation for non-conforming quadrilateral finite elements. Zbl 1071.65141Ainsworth, Mark 5 2005 Three-step \(h\)-\(p\) adaptive strategy for the incompressible Navier-Stokes equations. Zbl 0844.76057Oden, J. Tinsley; Wu, Weihan; Ainsworth, Mark 5 1995 The \(hp\)-MITC finite element method for the Reissner-Mindlin plate problem. Zbl 1058.74076Ainsworth, Mark; Pinchedez, Katia 5 2002 Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity. Zbl 1228.74076Ainsworth, Mark; Rankin, Richard 4 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 4 2012 A comparison of solvers for linear complementarity problems arising from large-scale masonry structures. Zbl 1164.74355Ainsworth, Mark; Mihai, L. Angela 4 2006 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 Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081Ainsworth, Mark; Glusa, Christian 4 2017 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 \(H^2\)-stable polynomial liftings on triangles. Zbl 1460.46020Ainsworth, Mark; Parker, Charles 4 2020 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 Modeling and numerical analysis of masonry structures. Zbl 1115.74036Ainsworth, Mark; Mihai, L. Angela 3 2007 The performance of Bank-Weiser’s error estimator for quadrilateral finite elements. Zbl 0807.65109Ainsworth, Mark 3 1994 Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043Ainsworth, Mark 3 1999 Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092Ainsworth, Mark; McLean, Bill; Tran, Thanh 3 2000 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 Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050Sherwin, Spencer J.; Ainsworth, Mark 3 2000 Preconditioning the mass matrix for high order finite element approximation on tetrahedra. Zbl 1466.65174Ainsworth, Mark; Jiang, Shuai 3 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 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 56 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 2 2020 Some remarks on spectral convergence and stability of iso-geometric analysis. Zbl 07337902Ainsworth, Mark; Davydov, Oleg; Wang, Hongrui 1 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. 7 2019 A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems. Zbl 1441.65090Ainsworth, Mark; Vejchodský, Tomáš 6 2019 Multilevel techniques for compression and reduction of scientific data – the multivariate case. Zbl 1428.65074Ainsworth, Mark; Tugluk, Ozan; Whitney, Ben; Klasky, Scott 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 24 2018 Hybrid finite element-spectral method for the fractional Laplacian: approximation theory and efficient solver. Zbl 1402.65148Ainsworth, Mark; Glusa, Christian 20 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 62 2017 Well-posedness of the Cahn-Hilliard equation with fractional free energy and its Fourier Galerkin approximation. Zbl 1422.65219Ainsworth, Mark; Mao, Zhiping 21 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 19 2017 Is the multigrid method fault tolerant? the two-grid case. Zbl 1365.65081Ainsworth, Mark; Glusa, Christian 4 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 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. 10 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. 59 2015 Tempered fractional Sturm-Liouville eigenproblems. Zbl 1323.34012Zayernouri, Mohsen; Ainsworth, Mark; Karniadakis, George Em 38 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 Pyramid algorithms for Bernstein-Bézier finite elements of high, nonuniform order in any dimension. Zbl 1322.65102Ainsworth, Mark 7 2014 Robust error bounds for finite element approximation of reaction-diffusion problems with non-constant reaction coefficient in arbitrary space dimension. Zbl 1425.65140Ainsworth, Mark; Vejchodský, Tomáš 6 2014 On the adaptive selection of the parameter in stabilized finite element approximations. Zbl 1276.65076Ainsworth, 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 1455.65207Ainsworth, 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 14 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 4 2012 Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures. Zbl 1237.65120Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg 45 2011 Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems. Zbl 1229.65194Ainsworth, Mark; Vejchodský, Tomáš 13 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 4 2011 Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. Zbl 1213.65129Ainsworth, Mark; Wajid, Hafiz Abdul 33 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 30 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 17 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 56 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. 76 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 62 2005 Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow. Zbl 1078.76041Dörfler, W.; Ainsworth, M. 25 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 108 2004 Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. Zbl 1074.65112Ainsworth, Mark 86 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 41 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 11 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 18 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 722 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 18 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 Diagonal scaling of stiffness matrices in the Galerkin boundary element method. Zbl 0966.65092Ainsworth, Mark; McLean, Bill; Tran, Thanh 3 2000 Unsteady Navier-Stokes solvers using hybrid spectral/\(hp\) element methods. Zbl 0995.76050Sherwin, 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 0977.65093Cao, 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 36 1999 The approximation theory for the \(p\)-version finite element method and application to nonlinear elliptic PDEs. Zbl 0938.65122Ainsworth, Mark; Kay, David 20 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 Identification and a posteriori estimation of transported errors in finite element analysis. Zbl 0953.76043Ainsworth, 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 1 1999 Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114Ainsworth, Mark; Babuska, Ivo 44 1998 An adaptive refinement strategy for \(hp\)-finite element computations. Zbl 0895.65052Ainsworth, Mark; Senior, Bill 34 1998 ...and 23 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,729 Authors 69 Ainsworth, Mark 33 Oden, John Tinsley 32 Vohralík, Martin 31 Carstensen, Carsten 31 Demkowicz, Leszek F. 26 Zhang, Zhimin 24 Díez, Pedro 24 Praetorius, Dirk 21 Nicaise, Serge 19 Baccouch, Mahboub 18 Huang, Yunqing 17 Babuška, Ivo 17 Karniadakis, George Em 17 Li, Jichun 17 Repin, Sergeĭ Igorevich 16 Otárola, Enrique 15 Heuer, Norbert 15 Huerta, Antonio 14 Wang, Hong 13 Gudi, Thirupathi 13 Ladevèze, Pierre 13 Parés, Núria 12 Calo, Victor Manuel 12 Ern, Alexandre 12 Führer, Thomas 12 Karkulik, Michael 12 Liu, Steve Wenbin 12 Picasso, Marco 12 Schöberl, Joachim 12 Zayernouri, Mohsen 11 Allendes, Alejandro 11 Bespalov, Alexei 11 Chan, Jesse 11 Gatica, Gabriel N. 11 Hoppe, Ronald H. W. 11 Melenk, Jens Markus 11 Schroder, Andreas 11 Strouboulis, Theofanis 11 Yang, Yidu 10 Hauke, Guillermo 10 Houston, Paul 10 Nochetto, Ricardo Horacio 10 Patera, Anthony T. 10 Rankin, Richard 10 Sauter, Stefan A. 10 Stein, Erwin 9 Adjerid, Slimane 9 Cai, Zhiqiang 9 Deng, Quanling 9 Düster, Alexander 9 Georgoulis, Emmanuil H. 9 Guo, Hailong 9 Kim, Kwang Yeon 9 Merdon, Christian 9 Pardo, David 9 Rank, Ernst 9 Ródenas, Juan José 9 Tavener, Simon J. 9 van der Vegt, Jaap J. W. 9 Wheeler, Mary Fanett 9 Wick, Thomas 9 Yan, Ningning 9 Zhang, Shun 8 Bordas, Stéphane Pierre Alain 8 Carey, Graham Francis 8 Chamoin, Ludovic 8 Chaudhry, Jehanzeb Hameed 8 Chen, Yanping 8 Creusé, Emmanuel 8 Du, Yu 8 Ervin, Vincent J. 8 Estep, Donald J. 8 Feischl, Michael 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 Wu, Haijun 8 Xu, Yifeng 8 Zhou, Jianwei 8 Zou, Qingsong 7 Abdulle, Assyr 7 Beirão da Veiga, Lourenço 7 Beuchler, Sven 7 Bi, Hai 7 D’Elia, Marta 7 Du, Shaohong 7 Fuenmayor, Francisco Javier 7 Giani, Stefano 7 Hiptmair, Ralf 7 Idesman, Alexander V. 7 Lamichhane, Bishnu Prasad 7 Ledger, Paul David 7 Mao, Shipeng 7 Mao, Zhiping ...and 2,629 more Authors all top 5 Cited in 185 Serials 384 Computer Methods in Applied Mechanics and Engineering 139 Journal of Computational Physics 137 Journal of Scientific Computing 136 Computers & Mathematics with Applications 104 Journal of Computational and Applied Mathematics 96 Numerische Mathematik 87 Applied Numerical Mathematics 83 International Journal for Numerical Methods in Engineering 74 Mathematics of Computation 72 SIAM Journal on Scientific Computing 69 SIAM Journal on Numerical Analysis 50 Computational Mechanics 41 Numerical Methods for Partial Differential Equations 40 Applied Mathematics and Computation 38 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 23 Computers and Fluids 22 Engineering Analysis with Boundary Elements 21 Computational Methods in Applied Mathematics 20 M\(^3\)AS. 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Terceira Série 2 Journal of Computational Acoustics 2 Boundary Value Problems ...and 85 more Serials all top 5 Cited in 40 Fields 1,879 Numerical analysis (65-XX) 879 Partial differential equations (35-XX) 425 Fluid mechanics (76-XX) 420 Mechanics of deformable solids (74-XX) 142 Optics, electromagnetic theory (78-XX) 113 Calculus of variations and optimal control; optimization (49-XX) 70 Real functions (26-XX) 57 Ordinary differential equations (34-XX) 46 Approximations and expansions (41-XX) 29 Probability theory and stochastic processes (60-XX) 26 Operator theory (47-XX) 24 Computer science (68-XX) 24 Geophysics (86-XX) 23 Statistical mechanics, structure of matter (82-XX) 22 Classical thermodynamics, heat transfer (80-XX) 20 Integral equations (45-XX) 20 Biology and other natural sciences (92-XX) 15 Global analysis, analysis on manifolds (58-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Functional analysis (46-XX) 13 Statistics (62-XX) 12 Special functions (33-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 8 Operations research, mathematical programming (90-XX) 8 Systems theory; control (93-XX) 7 Potential theory (31-XX) 5 Mechanics of particles and systems (70-XX) 5 Quantum theory (81-XX) 5 Information and communication theory, circuits (94-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 Differential geometry (53-XX) 2 Relativity and gravitational theory (83-XX) 1 Group theory and generalizations (20-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year