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.
Thomas P. Wihler
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|Peer Reviewed||Not Peer Reviewed|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|
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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