Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul

Abstract

In this paper we consider the a posteriori and a priori error analysis of discontinuous Galerkin interior penalty methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes. In particular, we discuss the question of error estimation for linear target functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement. The theoretical results are illustrated by a series of numerical experiments.

Citation

Georgoulis, E. H., Hall, E., & Houston, P. Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes

• Journal Article Type: Article
• Publication Date: Jan 1, 2006
• Deposit Date: Oct 23, 2006
• Publicly Available Date: Oct 9, 2007
• Peer Reviewed: Not Peer Reviewed
• Keywords: Anisotropic mesh adaptation, discontinuous Galerkin methods, PDEs with nonnegative characteristic form
• Public URL: https://nottingham-repository.worktribe.com/output/1018887