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Discrete maximum principle for interior penalty discontinuous Galerkin methods

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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.

Implicit a posteriori error estimation using patch recovery techniques

100%

Horváth T., Izsák F.

Open Mathematics

2012

tom 10

nr 1

55-72

We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.

Ograniczanie wyników

2 Open Mathematics

2 Horváth T.

1 Izsák F.

1 Mincsovics M.

1 2013

1 2012

Wyniki wyszukiwania

Discrete maximum principle for interior penalty discontinuous Galerkin methods

Implicit a posteriori error estimation using patch recovery techniques