A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

Houston, Paul and Suli, Endre and Wihler, Thomas P. (2006) A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems.

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Abstract

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Item Type: Article
Uncontrolled Keywords: hp-adaptivity, a-posteriori error analysis, discontinuous Galerkin finite elemenet methods, quasilinear elliptic PDEs
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 08 Sep 2006
Last Modified: 27 Jun 2011 10:14
URI: http://eprints.nottingham.ac.uk/id/eprint/413

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