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

Congreve, Scott and Houston, Paul and Wihler, Thomas P. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. Journal of Scientific Computing . ISSN 0885-7474 (Submitted)

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Official URL: http://www.springer.com/mathematics/computational+science+%26+engineering/journal/10915

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.

Item Type:Article
Additional Information:The original publication is available at www.springerlink.com
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:1493
Deposited By:Houston, Paul
Deposited On:12 Aug 2011 18:10
Last Modified:12 Aug 2011 18:10

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