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Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs

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

Authors

Scott Congreve

PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Professor of Computational and Applied Maths

Thomas P. Wihler



Abstract

In this article we propose a class of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of monotone type. The key idea in this setting is to first discretise the underlying nonlinear problem on a coarse finite element space V_{H,P}. The resulting `coarse' numerical solution is then exploited to provide the necessary data needed to linearise the underlying discretisation on the finer space V_{h,p}; thereby, only a linear system of equations is solved on the richer space V_{h,p}. In this article both the a priori and a posteriori error analysis of the two-grid hp-version discontinuous Galerkin finite element method is developed. Moreover, we propose and implement an hp-adaptive two-grid algorithm, which is capable of designing both the coarse and fine finite element spaces V_{H,P} and V_{h,p}, respectively, in an automatic fashion. Numerical experiments are presented for both two- and three-dimensional problems; in each case, we demonstrate that the cpu time required to compute the numerical solution to a given accuracy is typically less when the two-grid approach is exploited, when compared to the standard discontinuous Galerkin method.

Citation

Congreve, S., Houston, P., & Wihler, T. P. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Manuscript submitted for publication

Journal Article Type Article
Deposit Date Aug 12, 2011
Publicly Available Date Mar 28, 2024
Peer Reviewed Not Peer Reviewed
Public URL https://nottingham-repository.worktribe.com/output/1025989
Additional Information The original publication is available at www.springerlink.com

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