Ainsworth, Mark; Glusa, Christian The resiliency of multilevel methods on next-generation computing platforms: probabilistic model and its analysis. (English) Zbl 1464.65261 Singh, Vinai K. (ed.) et al., Advances in mathematical methods and high performance computing. Cham: Springer. Adv. Mech. Math. 41, 283-294 (2019). MSC: 65N55 65N30 65N75 65N50 65C30 65F10 65N12 65Y05 15B52 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{C. Glusa}, Adv. Mech. Math. 41, 283--294 (2019; Zbl 1464.65261) Full Text: DOI Link
Ainsworth, Mark; Mao, Zhiping Analysis and approximation of gradient flows associated with a fractional order Gross-Pitaevskii free energy. (English) Zbl 1449.65302 Commun. Appl. Math. Comput. 1, No. 1, 5-19 (2019). MSC: 65N12 65N30 65N50 35R11 26A33 35Q55 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{Z. Mao}, Commun. Appl. Math. Comput. 1, No. 1, 5--19 (2019; Zbl 1449.65302) Full Text: DOI
Ainsworth, Mark; Glusa, Christian Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver. (English) Zbl 1439.65142 Comput. Methods Appl. Mech. Eng. 327, 4-35 (2017). MSC: 65N30 35B45 35R11 65N22 65N55 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{C. Glusa}, Comput. Methods Appl. Mech. Eng. 327, 4--35 (2017; Zbl 1439.65142) Full Text: DOI arXiv
Ainsworth, Mark; Fu, Guosheng A lowest-order composite finite element exact sequence on pyramids. (English) Zbl 1439.74381 Comput. Methods Appl. Mech. Eng. 324, 110-127 (2017). MSC: 74S05 65N30 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{G. Fu}, Comput. Methods Appl. Mech. Eng. 324, 110--127 (2017; Zbl 1439.74381) Full Text: DOI arXiv
Ainsworth, Mark; Barrenechea, Gabriel R.; Wachtel, Andreas Stabilization of high aspect ratio mixed finite elements for incompressible flow. (English) Zbl 1322.76038 SIAM J. Numer. Anal. 53, No. 2, 1107-1120 (2015). MSC: 76M10 65N12 65N30 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., SIAM J. Numer. Anal. 53, No. 2, 1107--1120 (2015; Zbl 1322.76038) Full Text: DOI Link
Ainsworth, Mark; Rankin, Richard Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. (English) Zbl 1208.65156 IMA J. Numer. Anal. 31, No. 1, 254-280 (2011). MSC: 65N15 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{R. Rankin}, IMA J. Numer. Anal. 31, No. 1, 254--280 (2011; Zbl 1208.65156) Full Text: DOI Link
Ainsworth, Mark; Demkowicz, Leszek; Kim, Chang-Wan Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes. (English) Zbl 1173.76424 Comput. Methods Appl. Mech. Eng. 196, No. 37-40, 3493-3507 (2007). MSC: 76V05 76M10 65N30 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., Comput. Methods Appl. Mech. Eng. 196, No. 37--40, 3493--3507 (2007; Zbl 1173.76424) Full Text: DOI
Ainsworth, Mark A posteriori error estimation for lowest order Raviart-Thomas mixed finite elements. (English) Zbl 1159.65353 SIAM J. Sci. Comput. 30, No. 1, 189-204 (2007). MSC: 65N15 35J25 65N30 35J05 35Q60 65N50 65N55 PDFBibTeX XMLCite \textit{M. Ainsworth}, SIAM J. Sci. Comput. 30, No. 1, 189--204 (2007; Zbl 1159.65353) Full Text: DOI
Ainsworth, Mark A posteriori error estimation for discontinuous Galerkin finite element approximation. (English) Zbl 1151.65083 SIAM J. Numer. Anal. 45, No. 4, 1777-1798 (2007). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65N15 65N30 65N50 35J05 PDFBibTeX XMLCite \textit{M. Ainsworth}, SIAM J. Numer. Anal. 45, No. 4, 1777--1798 (2007; Zbl 1151.65083) Full Text: DOI
Ainsworth, Mark Robust a posteriori error estimation for nonconforming finite element approximation. (English) Zbl 1085.65102 SIAM J. Numer. Anal. 42, No. 6, 2320-2341 (2005). Reviewer: Dietrich Braess (Bochum) MSC: 65N15 65N12 65N50 65N30 35J25 PDFBibTeX XMLCite \textit{M. Ainsworth}, SIAM J. Numer. Anal. 42, No. 6, 2320--2341 (2005; Zbl 1085.65102) Full Text: DOI
Ainsworth, Mark A posteriori error estimation for non-conforming quadrilateral finite elements. (English) Zbl 1071.65141 Int. J. Numer. Anal. Model. 2, No. 1, 1-18 (2005). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N15 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth}, Int. J. Numer. Anal. Model. 2, No. 1, 1--18 (2005; Zbl 1071.65141)
Ainsworth, Mark Discrete dispersion relation for \(hp\)-version finite element approximation at high wave number. (English) Zbl 1074.65112 SIAM J. Numer. Anal. 42, No. 2, 553-575 (2004). Reviewer: Myron Sussman (Bethel Park) MSC: 65M50 65M15 65M60 PDFBibTeX XMLCite \textit{M. Ainsworth}, SIAM J. Numer. Anal. 42, No. 2, 553--575 (2004; Zbl 1074.65112) Full Text: DOI
Ainsworth, Mark; Coyle, Joe Hierarchic finite element bases on unstructured tetrahedral meshes. (English) Zbl 1042.65088 Int. J. Numer. Methods Eng. 58, No. 14, 2103-2130 (2003). Reviewer: J. Lovíšek (Bratislava) MSC: 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{J. Coyle}, Int. J. Numer. Methods Eng. 58, No. 14, 2103--2130 (2003; Zbl 1042.65088) Full Text: DOI Link
Ainsworth, Mark; McLean, William Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. (English) Zbl 1073.65132 Numer. Math. 93, No. 3, 387-413 (2003). Reviewer: José Mas (Valéncia) MSC: 65N38 65F35 65N55 65F10 65N50 65N30 35J25 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{W. McLean}, Numer. Math. 93, No. 3, 387--413 (2003; Zbl 1073.65132) Full Text: DOI
Ainsworth, Mark; Kelly, Donald W. A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous Dirichlet problem. (English) Zbl 0999.65116 Adv. Comput. Math. 15, No. 1-4, 3-23 (2001). Reviewer: Erwin Schechter (Kaiserslautern) MSC: 65N15 35J05 65N50 65N30 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{D. W. Kelly}, Adv. Comput. Math. 15, No. 1--4, 3--23 (2001; Zbl 0999.65116) Full Text: DOI
Ainsworth, M.; Dörfler, W. Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy. (English) Zbl 0988.65096 Computing 66, No. 2, 199-229 (2001). Reviewer: Dinh Nho Hao (Frankfurt am Main) MSC: 65N12 35B25 35J25 65N50 65N15 65N06 65N30 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{W. Dörfler}, Computing 66, No. 2, 199--229 (2001; Zbl 0988.65096) Full Text: DOI
Ainsworth, Mark; Senior, Bill \(hp\)-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. (English) Zbl 0941.65113 Bern, Marshall W. (ed.) et al., Grid generation and adaptive algorithms. Proceedings of a workshop, integral part of 1996-97 IMA program, Minnesota Univ., Minneapolis, MN, USA, April 28 - May 2, 1997. New York, NY: Springer. IMA Vol. Math. Appl. 113, 1-27 (1999). MSC: 65N30 65N12 65N50 35J05 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{B. Senior}, IMA Vol. Math. Appl. 113, 1--27 (1999; Zbl 0941.65113)
Ainsworth, Mark; McLean, William; Tran, Thanh The conditioning of boundary element equations on locally refined meshes and preconditioning by diagonal scaling. (English) Zbl 0947.65125 SIAM J. Numer. Anal. 36, No. 6, 1901-1932 (1999). Reviewer: R.H.W.Hoppe (München) MSC: 65N38 65N50 45E10 65R20 35J25 65F35 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., SIAM J. Numer. Anal. 36, No. 6, 1901--1932 (1999; Zbl 0947.65125) Full Text: DOI
Ainsworth, Mark; Senior, Bill An adaptive refinement strategy for \(hp\)-finite element computations. (English) Zbl 0895.65052 Appl. Numer. Math. 26, No. 1-2, 165-178 (1998). Reviewer: P.Burda (Praha) MSC: 65N30 35J25 65Y20 65N12 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{B. Senior}, Appl. Numer. Math. 26, No. 1--2, 165--178 (1998; Zbl 0895.65052) Full Text: DOI
Ainsworth, Mark; Senior, Bill Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers. (English) Zbl 0906.73057 Comput. Methods Appl. Mech. Eng. 150, No. 1-4, 65-87 (1997). MSC: 74S05 74R99 74B05 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{B. Senior}, Comput. Methods Appl. Mech. Eng. 150, No. 1--4, 65--87 (1997; Zbl 0906.73057) Full Text: DOI
Ainsworth, M.; Kelly, D. W.; Sloan, I. H.; Wang, S. L. Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem. (English) Zbl 0890.65109 IMA J. Numer. Anal. 17, No. 4, 547-561 (1997). Reviewer: J.P.Milaszewicz (Dublin) MSC: 65N15 65N30 35J65 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., IMA J. Numer. Anal. 17, No. 4, 547--561 (1997; Zbl 0890.65109) Full Text: DOI
Ainsworth, Mark; Senior, Bill; Andrews, Derek Preconditioners for the adaptive \(hp\) version finite element method. (English) Zbl 0870.65110 Whiteman, J. R. (ed.), The mathematics of finite elements and applications. Highlights 1996. Proceedings of the 9th conference, MAFELAP 1996, Uxbridge, GB, June 25–28, 1996, Chichester: Wiley. 81-91 (1997). MSC: 65N55 65F10 65N30 35J05 65F35 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., in: The mathematics of finite elements and applications. Highlights 1996. Proceedings of the 9th conference, MAFELAP 1996, Uxbridge, GB, June 25--28, 1996,. Chichester: Wiley. 81--91 (1997; Zbl 0870.65110)
Ainsworth, Mark A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. (English) Zbl 0860.65111 SIAM J. Sci. Comput. 17, No. 6, 1395-1413 (1996). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65N30 65N55 65F10 35J25 65F35 65N50 PDFBibTeX XMLCite \textit{M. Ainsworth}, SIAM J. Sci. Comput. 17, No. 6, 1395--1413 (1996; Zbl 0860.65111) Full Text: DOI
Zienkiewicz, O. C.; Zhu, J. Z.; Craig, A. W.; Ainsworth, M. Simple and practical error estimation and adaptivity: h and h-p version procedures. (English) Zbl 0693.73047 Adaptive methods for partial differential equations, Proc. Workshop, Troy/NY (USA) 1988, 100-114 (1989). MSC: 74S05 65N30 65N15 PDFBibTeX XML