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Discrete maximum principle for interior penalty discontinuous Galerkin methods

100%

Horváth T., Mincsovics M.

Open Mathematics

2013

tom 11

nr 4

664-679

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.

The discrete maximum principle for Galerkin solutions of elliptic problems

100%

Vejchodský T.

Open Mathematics

2012

tom 10

nr 1

25-43

This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys the state of the art in the field of the discrete maximum principle and provides new generalizations of several results.

Ograniczanie wyników

2 Open Mathematics

1 Horváth T.

1 Mincsovics M.

1 Vejchodský T.

1 2013

1 2012

Wyniki wyszukiwania

Discrete maximum principle for interior penalty discontinuous Galerkin methods

The discrete maximum principle for Galerkin solutions of elliptic problems