Discontinuous Galerkin methods for problems with Dirac delta source
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, p. 1467-1483

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.

DOI : https://doi.org/10.1051/m2an/2012010
Classification:  65N30
Keywords: elliptic pdes, discontinuous Galerkin methods, Dirac delta source
@article{M2AN_2012__46_6_1467_0,
author = {Houston, Paul and Wihler, Thomas Pascal},
title = {Discontinuous Galerkin methods for problems with Dirac delta source},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
pages = {1467-1483},
doi = {10.1051/m2an/2012010},
zbl = {1272.65092},
mrnumber = {2996336},
language = {en},
url = {http://www.numdam.org/item/M2AN_2012__46_6_1467_0}
}

Houston, Paul; Wihler, Thomas Pascal. Discontinuous Galerkin methods for problems with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 46 (2012) no. 6, pp. 1467-1483. doi : 10.1051/m2an/2012010. http://www.numdam.org/item/M2AN_2012__46_6_1467_0/

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