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Second-order elliptic PDE with discontinuous boundary data

Houston, Paul; Wihler, Thomas P.

Authors

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Thomas P. Wihler wihler@math.unibe.ch



Abstract

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Citation

Houston, P., & Wihler, T. P. Second-order elliptic PDE with discontinuous boundary data. Manuscript submitted for publication

Journal Article Type Article
Deposit Date Jan 15, 2010
Journal IMA Journal of Numerical Analysis
Print ISSN 0272-4979
Electronic ISSN 0272-4979
Publisher Oxford University Press (OUP)
Peer Reviewed Not Peer Reviewed
Public URL http://eprints.nottingham.ac.uk/id/eprint/1215
Publisher URL http://imajna.oxfordjournals.org/
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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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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