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Two‐Grid hp ‐Version DGFEMs for Strongly Monotone Second‐Order Quasilinear Elliptic PDEs
Author(s) -
Congreve Scott,
Houston Paul,
Wihler Thomas P.
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110002
Subject(s) - discretization , monotone polygon , discontinuous galerkin method , mathematics , finite element method , partial differential equation , a priori and a posteriori , nonlinear system , space (punctuation) , galerkin method , grid , mathematical analysis , order (exchange) , elliptic partial differential equation , numerical analysis , computer science , geometry , physics , epistemology , quantum mechanics , economics , thermodynamics , operating system , philosophy , finance
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. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)