# Discrete maximum principle for interior penalty discontinuous Galerkin methods

Tamás Horváth; Miklós Mincsovics

Open Mathematics (2013)

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

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topTamás 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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