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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

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.

Journal Article Type Article
Journal IMA Journal of Numerical Analysis
Print ISSN 0272-4979
Electronic ISSN 0272-4979
Publisher Oxford University Press (OUP)
Peer Reviewed Not Peer Reviewed
APA6 Citation Houston, P., & Wihler, T. P. Second-order elliptic PDE with discontinuous boundary data. Manuscript submitted for publication
Publisher URL http://imajna.oxfordjournals.org/
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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