Discontinuous Galerkin methods for problems with Dirac delta source
Houston, Paul and Wihler, Thomas P. (2011) Discontinuous Galerkin methods for problems with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis . ISSN 0764-583X (Submitted)
Official URL: http://www.esaim-m2an.org/action/displayJournal?jid=MZA
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.
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