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

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

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.