Local parameter selection in the C0 interior penalty method for the biharmonic equation
Author:
Bringmann Philipp1, Carstensen Carsten2, Streitberger Julian1
Affiliation:
1. Institute of Analysis and Scientific Computing , TU Wien , Austria 2. Department of Mathematics, Humboldt-Universität zu Berlin , Berli , Germany
Abstract
Abstract
The symmetric 0 interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the geometry of the underlying triangulation for arbitrary polynomial degrees. The proposed choice ensures a stable discretization with guaranteed discrete ellipticity constant. Numerical evidence for uniform and adaptive mesh-refinement and various polynomial degrees supports the reliability and efficiency of the local parameter selection and recommends this in practice. The approach is documented in 2D for triangles, but the methodology behind can be generalized to higher dimensions, to non-uniform polynomial degrees, and to rectangular discretizations. An appendix presents the realization of our proposed parameter selection in various established finite element software packages. a detailed documentation of C0 interior penalty method in.
Publisher
Walter de Gruyter GmbH
Subject
Computational Mathematics,Numerical Analysis
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