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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 pmxsc@nottingham.ac.uk

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Thomas P. Wihler wihler@math.unibe.ch



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
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 0885-7474
Publisher Humana Press
Peer Reviewed Not Peer Reviewed
Public URL http://eprints.nottingham.ac.uk/id/eprint/1493
Publisher URL http://www.springer.com/mathematics/computational+science+%26+engineering/journal/10915
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
Additional Information The original publication is available at www.springerlink.com

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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