Scott Congreve
Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs
Congreve, Scott; Houston, Paul; Wihler, Thomas P.
Authors
Professor PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Head of School (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 |
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Deposit Date | Aug 12, 2011 |
Peer Reviewed | Not Peer Reviewed |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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