Mixed Discontinuous Galerkin Methods with Minimal Stabilization

Daniele Marazzina

Abstract


In this talk we will address the problem of finding the minimal necessary stabilization
for a class of Discontinuous Galerkin (DG) methods in mixed form. In particular, we will
consider the Poisson problem and present a new stabilized formulation of the Bassi-Rebay
method and a new formulation of the Local Discontinuous Galerkin (LDG) method.
It will be shown that, in order to reach stability, it is enough to add jump terms only
over a part of the boundary of the domain, instead of over all the skeleton of the mesh,
as it is usually done (see the original LDG method, for instance).
We will also support our theory with numerical results.

[DOI: 10.1685/CSC06108] About DOI

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DOI: http://dx.doi.org/10.1685/




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