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Discontinuous Galerkin methods for problems with Dirac delta source∗

Published online by Cambridge University Press:  31 May 2012

Paul Houston  and
Thomas Pascal Wihler
Paul Houston
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Paul.Houston@nottingham.ac.uk
Thomas Pascal Wihler
Affiliation:
Mathematics Institute, University of Bern, 3012 Bern, Switzerland; wihler@math.unibe.ch
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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 L2-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.

Keywords

Elliptic PDEsdiscontinuous Galerkin methodsDirac delta source
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1467 - 1483
Copyright
© EDP Sciences, SMAI, 2012

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