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Discontinuous Galerkin methods for problems with Dirac delta source

Houston, Paul; Wihler, Thomas P.


Professor of Computational and Applied Maths

Thomas P. Wihler


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.


Houston, P., & Wihler, T. P. Discontinuous Galerkin methods for problems with Dirac delta source. Manuscript submitted for publication

Journal Article Type Article
Deposit Date Aug 12, 2011
Journal ESAIM: Mathematical Modelling and Numerical Analysis
Print ISSN 0764-583X
Electronic ISSN 0764-583X
Publisher EDP Open
Peer Reviewed Not Peer Reviewed
Public URL
Publisher URL
Additional Information Copyright EDP Sciences.


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