Discontinuous Galerkin methods for problems with Dirac delta source∗

Paul Houston; Thomas Pascal Wihler

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1467-1483
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Houston, Paul, and Wihler, Thomas Pascal. "Discontinuous Galerkin methods for problems with Dirac delta source∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1467-1483. <http://eudml.org/doc/276387>.

@article{Houston2012,
abstract = {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.},
author = {Houston, Paul, Wihler, Thomas Pascal},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Elliptic PDEs; discontinuous Galerkin methods; Dirac delta source; discontinous Galerkin methods; a priori error bound; numerical results; finite element; linear second-order elliptic PDE},
language = {eng},
month = {5},
number = {6},
pages = {1467-1483},
publisher = {EDP Sciences},
title = {Discontinuous Galerkin methods for problems with Dirac delta source∗},
url = {http://eudml.org/doc/276387},
volume = {46},
year = {2012},
}

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
DA - 2012/5//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1467
EP - 1483
AB - 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.
LA - eng
KW - Elliptic PDEs; discontinuous Galerkin methods; Dirac delta source; discontinous Galerkin methods; a priori error bound; numerical results; finite element; linear second-order elliptic PDE
UR - http://eudml.org/doc/276387
ER -

References

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