Discontinuous Galerkin methods for problems with Dirac delta source
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 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 : 10.1051/m2an/2012010
Classification : 65N30
Mots-clés : elliptic pdes, discontinuous Galerkin methods, Dirac delta source 
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     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},
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     zbl = {1272.65092},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2012010/}
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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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