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Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs

Congreve, Scott; Houston, Paul; Wihler, Thomas P.

Authors

Scott Congreve pmxsc@nottingham.ac.uk

Paul Houston Paul.Houston@nottingham.ac.uk

Thomas P. Wihler wihler@math.unibe.ch



Abstract

In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(H,P). The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(h,p); thereby, only a linear system of equations is solved on the richer space V(h,p). Numerical experiments confirming the theoretical results are presented.

Journal Article Type Article
Publication Date Jan 1, 2011
Journal Proceedings in Applied Mathematics and Mechanics
Electronic ISSN 1617-7061
Publisher Wiley-VCH Verlag
Peer Reviewed Peer Reviewed
Volume 11
Issue 1
APA6 Citation Congreve, S., Houston, P., & Wihler, T. P. (2011). Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. PAMM, 11(1), doi:10.1002/pamm.201110002
DOI https://doi.org/10.1002/pamm.201110002
Publisher URL http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110002/pdf
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Published as: Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs, Scott Congreve, Paul Houston and Thomas P.Wihler, Proceedings in Applied Mathematics and Mechanics, 11(1) Copyright © . 2011Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. (http://onlinelibrary.wi...1002/pamm.201110002/pdf )

Paper originally presented at: 82nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für Angewandte Mathematik und Mechanik), Technische Universität Graz 18-21 Apr. 2011.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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