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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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110002/pdf

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:Faculty of Science > School of Mathematical Sciences
ID Code:1481
Deposited By:Houston, Paul
Deposited On:06 Sep 2012 10:38
Last Modified:06 Sep 2012 10:38

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