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Discontinuous Galerkin methods for problems with Dirac deltasource∗

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 linearsecond-order elliptic partial differential equations with Dirac delta right-hand side. Inparticular, assuming that the underlying computational mesh is quasi-uniform, we derive ana priori bound on the error measured in terms of theL2-norm. Additionally, we develop residual-based aposteriori error estimators that can be used within an adaptive mesh refinementframework. Numerical examples for the symmetric interior penalty scheme are presentedwhich confirm the theoretical results.

Keywords

Elliptic PDEsdiscontinuous Galerkin methodsDirac delta source

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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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