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Title: Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
Authors: Georgoulis, Emmanuil H.
Hal, Edward
Houston, Paul
First Published: 2006
Publisher: Dept. of Mathematics, University of Leicester
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 outow 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.
Series/Report no.: MA 06-018
Type: Report
Appears in Collections:Reports, Dept. of Mathematics

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