| Issue |
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
|
|
|---|---|---|
| Page(s) | 1467 - 1483 | |
| DOI | https://doi.org/10.1051/m2an/2012010 | |
| Published online | 31 May 2012 | |
Discontinuous Galerkin methods for problems with Dirac delta source∗
1
School of Mathematical Sciences, University of Nottingham,
University Park, Nottingham, NG7
2RD, UK
Paul.Houston@nottingham.ac.uk
2
Mathematics Institute, University of Bern,
3012
Bern,
Switzerland
wihler@math.unibe.ch
Received:
17
June
2011
Revised:
22
November
2011
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.
Mathematics Subject Classification: 65N30
Key words: Elliptic PDEs / discontinuous Galerkin methods / Dirac delta source
© EDP Sciences, SMAI, 2012
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