The Mathematical Institute, University of Oxford, Eprints Archive

Discontinuous hp-Finite Element Methods for Advection-Diffusion Problems

Houston, P. and Schwab, Christoph and Suli, Endre (2000) Discontinuous hp-Finite Element Methods for Advection-Diffusion Problems. Technical Report. Unspecified. (Submitted)

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Abstract

We consider the hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form. This class of equations includes second--order elliptic and parabolic equations, first-order hyperbolic equations, as well as problems of mixed hyperbolic-elliptic-parabolic type. Our main concern is the error analysis of the method in the absence of streamline-diffusion stabilization. In the hyperbolic case, an hp-optimal error bound is derived. In the self-adjoint elliptic case, an error bound that is h-optimal and p-suboptimal by half a power of p is obtained. These estimates are then combined to deduce an error bound in the general case. For element-wise analytic solutions the method exhibits exponential rates of convergence under p-refinement. The theoretical results are illustrated by numerical experiments.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1266
Deposited By:Lotti Ekert
Deposited On:01 Jun 2011 09:19
Last Modified:01 Jun 2011 09:19

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