Discontinuous Galerkin methods for problems with Dirac delta source
Paul Houston, Thomas Pascal Wihler (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
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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 bound on the error measured in terms of the -norm. Additionally, we develop residual-based error estimators that can be used within an adaptive mesh refinement ...