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

Congreve, Scott and Houston, Paul and Wihler, Thomas P. (2011) Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proceedings in Applied Mathematics and Mechanics, 11 (1). pp. 3-6. ISSN 1617-7061

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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.

Item Type: Article
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.
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 06 Sep 2012 09:38
Last Modified: 06 Sep 2012 09:38
URI: http://eprints.nottingham.ac.uk/id/eprint/1481

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