Formulation of discontinuous Galerkin method with non-zero mesh skeleton width for scalar and vector elliptic problems [dataset]

Jan Jaskowiec
2015 Figshare  
The paper presents the Discontinuous Galerkin method (DG) formulated with a non-zero mesh skeleton width. The mesh skeleton has a finite volume but is not spatially discretized. Such an approach results in a novel formulation with inter-element interfaces which is named Interface Discontinuous Galerkin (IDG). The IDG approach, contrary to standard DG (SDG) approach, is symmetric and numerically stable. The IDG formulation is consistent and gives better results in comparison to the SDG method.
more » ... o the SDG method. In the IDG approach the interface law comes directly from the problem under consideration and has a physical interpretation. It provides compatibility conditions for the discontinuous finite element interpolation. In consequence, the penalty parameter present in the SDG method is substituted by a geometrically interpreted parameter that can be quite easily evaluated with the use of the approach described in the paper.
doi:10.6084/m9.figshare.1304147.v1 fatcat:ajf77hcdgjf7fl3qkv6rdfbl4e