Scott Congreve
Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs
Congreve, Scott; Houston, Paul; Wihler, Thomas P.
Authors
PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths
Thomas P. Wihler
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.
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), https://doi.org/10.1002/pamm.201110002
Journal Article Type | Article |
---|---|
Publication Date | Jan 1, 2011 |
Deposit Date | Sep 6, 2012 |
Publicly Available Date | Sep 6, 2012 |
Journal | Proceedings in Applied Mathematics and Mechanics |
Electronic ISSN | 1617-7061 |
Publisher | Wiley-VCH Verlag |
Peer Reviewed | Peer Reviewed |
Volume | 11 |
Issue | 1 |
DOI | https://doi.org/10.1002/pamm.201110002 |
Public URL | https://nottingham-repository.worktribe.com/output/1010513 |
Publisher URL | http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110002/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.wiley.com/doi/10.1002/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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