We address the problem of finding the necessary stabilization for a class of discontinuous Galerkin methods in mixed form for the 2D case. In particular, we present a new stabilized formulation of the (unstable) Bassi–Rebay method and a new formulation of the local discontinuous Galerkin method. The stability properties of the new formulations are studied and error estimates are derived. The theoretical results are validated in a series of numerical tests.
Stability Properties of Discontinuous Galerkin Methods for Two-Dimensional Elliptic Problems
MARAZZINA, DANIELE
2008-01-01
Abstract
We address the problem of finding the necessary stabilization for a class of discontinuous Galerkin methods in mixed form for the 2D case. In particular, we present a new stabilized formulation of the (unstable) Bassi–Rebay method and a new formulation of the local discontinuous Galerkin method. The stability properties of the new formulations are studied and error estimates are derived. The theoretical results are validated in a series of numerical tests.File in questo prodotto:
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