The Mathematical Institute, University of Oxford, Eprints Archive

hp-Finite Element Methods for Hyperbolic Problems

Suli, Endre and Houston, P. and Schwab, Christoph (1999) hp-Finite Element Methods for Hyperbolic Problems. Technical Report. Unspecified. (Submitted)

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Abstract

Presented as Invited Lecture at the 10th Conference on the Mathematics of Finite Elements and Applications, Brunel University, June 1999.

This paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial differential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diffusion problems, degenerate elliptic equations and second-order problems of mixed elliptic-hyperbolic-parabolic type. An a priori error bound is derived for the method in the so-called DG-norm which is optimal in terms of the mesh size h; the error bound is either 1 degree or 1/2 degree below optimal in terms of the polynomial degree p, depending on whether the problem is convection-dominated, or diffusion-dominated, respectively. In the case of a first-order hyperbolic equation the error bound is hp-optimal in the DG-norm. For first-order hyperbolic problems, we also discuss the a posteriori error analysis of the method and implement the resulting bounds into an hp-adaptive algorithm. The theoretical findings are illustrated by numerical experiments.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1289
Deposited By:Lotti Ekert
Deposited On:02 Jun 2011 08:58
Last Modified:02 Jun 2011 08:58

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