Bubble stabilized discontinuous Galerkin methods on conforming and non-conforming meshes

Authors:
Erik Burman;Benjamin Stamm
Affiliations:
Department of Mathematics, University of Sussex, Brighton, UK BN1 9RF;Department of Mathematics, University of California, Berkeley, United States 94720
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2011

Citing 9
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Abstract

The aim of this paper is to discuss the properties of the bubble stabilized discontinuous Galerkin method with respect to mesh geometry. First we show that on certain non-conforming meshes the bubble stabilized discontinuous Galerkin method allows for hanging nodes/edges. Then we consider the case of conforming meshes and present a post-processing algorithm based on the Crouzeix-Raviart method to obtain the Bubble Stabilized Discontinuous Galerkin (BSDG) method. Although finally the post-processed solution does not coincide with the BSDG-solution in general, they satisfy the same (approximation) properties and are close to each other. Moreover, the post-processed solution has continuous flux over the edges.