# 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

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topHouston, 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 -

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