# Discrete maximum principle for interior penalty discontinuous Galerkin methods

Open Mathematics (2013)

• Volume: 11, Issue: 4, page 664-679
• ISSN: 2391-5455

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## Abstract

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A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of these conditions. The theoretical results are illustrated with numerical examples.

## How to cite

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Tamás Horváth, and Miklós Mincsovics. "Discrete maximum principle for interior penalty discontinuous Galerkin methods." Open Mathematics 11.4 (2013): 664-679. <http://eudml.org/doc/269421>.

@article{TamásHorváth2013,
abstract = {A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of these conditions. The theoretical results are illustrated with numerical examples.},
author = {Tamás Horváth, Miklós Mincsovics},
journal = {Open Mathematics},
keywords = {Discrete maximum principle; Discontinuous Galerkin; Interior penalty; comparison principle; conservation of nonnegativity; -matrix; finite element; one-dimensional reaction-diffusion operator; interior penalty discontinuous Galerkin method; numerical example},
language = {eng},
number = {4},
pages = {664-679},
title = {Discrete maximum principle for interior penalty discontinuous Galerkin methods},
url = {http://eudml.org/doc/269421},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Tamás Horváth
AU - Miklós Mincsovics
TI - Discrete maximum principle for interior penalty discontinuous Galerkin methods
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 664
EP - 679
AB - A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of these conditions. The theoretical results are illustrated with numerical examples.
LA - eng
KW - Discrete maximum principle; Discontinuous Galerkin; Interior penalty; comparison principle; conservation of nonnegativity; -matrix; finite element; one-dimensional reaction-diffusion operator; interior penalty discontinuous Galerkin method; numerical example
UR - http://eudml.org/doc/269421
ER -

## References

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