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Burman, Erik; Stamm, Benjamin

Bubble stabilized discontinuous Galerkin methods on conforming and non-conforming meshes. (English) Zbl 1261.65114

Calcolo 48, No. 2, 189-209 (2011).
Authors’ 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.
Reviewer: Ali Filiz (Aydin)

Cited in 1 Document

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Keywords:

elliptic equation; bubble stabilized discontinuous Galerkin method; non-conforming meshes; post-processing algorithm; Crouzeix-Raviart method
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