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 -
References
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