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IMA Journal of Numerical Analysis Advance Access originally published online on November 27, 2007
IMA Journal of Numerical Analysis 2008 28(3):552-579; doi:10.1093/imanum/drm020
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Stability properties of discontinuous Galerkin methods for 2D elliptic problems

Daniele Marazzina{dagger}

Dipartimento di Scienze Economiche e Metodi Quantitativi, Università degli Studi del Piemonte Orientale A. Avogadro, Via Perrone 18, 28100 Novara, Italy

{dagger} Email: daniele.marazzina{at}unipv.it

Received on 17 November 2006. Revised on 7 June 2007.


  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.

Key Words: Bassi–Rebay method; discontinuous Galerkin finite elements; LDG method; stability


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