Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

Georgoulis, Emmanuil H. and Hall, Edward and Houston, Paul Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity. Applied Numerical Mathematics . (Submitted)

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Abstract

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms 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 and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 17 Oct 2007 13:22
Last Modified: 27 Jun 2011 10:20
URI: http://eprints.nottingham.ac.uk/id/eprint/670

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