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

Houston, Paul; Suli, Endre; Wihler, Thomas P.

Authors

Paul Houston

Endre Suli

Thomas P. Wihler



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.

Journal Article Type Article
Publication Date Jan 1, 2006
Peer Reviewed Not Peer Reviewed
APA6 Citation Houston, P., Suli, E., & Wihler, T. P. (2006). A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems
Keywords hp-adaptivity, a-posteriori error analysis, discontinuous Galerkin finite elemenet methods, quasilinear elliptic PDEs
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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