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

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

Authors

Emmanuil H. Georgoulis

Edward Hall

Paul Houston



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.

Journal Article Type Article
Publication Date Jan 1, 2006
Peer Reviewed Not Peer Reviewed
APA6 Citation Georgoulis, E. H., Hall, E., & Houston, P. (2006). Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
Keywords Anisotropic mesh adaptation, discontinuous Galerkin methods, PDEs with nonnegative characteristic form
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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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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