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Discontinuous Galerkin methods for problems with Dirac delta source

Houston, Paul; Wihler, Thomas P.

Authors

Paul Houston Paul.Houston@nottingham.ac.uk

Thomas P. Wihler wihler@math.unibe.ch



Abstract

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L^2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement framework. Numerical examples for the symmetric interior penalty scheme are presented which confirm the theoretical results.

Journal Article Type Article
Journal ESAIM: Mathematical Modelling and Numerical Analysis
Print ISSN 0764-583X
Electronic ISSN 0764-583X
Publisher EDP Open
Peer Reviewed Not Peer Reviewed
APA6 Citation Houston, P., & Wihler, T. P. Discontinuous Galerkin methods for problems with Dirac delta source. Manuscript submitted for publication
Publisher URL http://www.esaim-m2an.org/action/displayJournal?jid=MZA
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Copyright EDP Sciences.

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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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