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.
Mots clés : 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 }, pages = {1467--1483}, publisher = {EDP-Sciences}, volume = {46}, number = {6}, year = {2012}, doi = {10.1051/m2an/2012010}, mrnumber = {2996336}, zbl = {1272.65092}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2012010/} }
TY - JOUR AU - Houston, Paul AU - Wihler, Thomas Pascal TI - Discontinuous Galerkin methods for problems with Dirac delta source JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 1467 EP - 1483 VL - 46 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012010/ DO - 10.1051/m2an/2012010 LA - en ID - M2AN_2012__46_6_1467_0 ER -
%0 Journal Article %A Houston, Paul %A Wihler, Thomas Pascal %T Discontinuous Galerkin methods for problems with Dirac delta source %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1467-1483 %V 46 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012010/ %R 10.1051/m2an/2012010 %G en %F 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 , Tome 46 (2012) no. 6, pp. 1467-1483. doi : 10.1051/m2an/2012010. http://www.numdam.org/articles/10.1051/m2an/2012010/
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