Stabilization mechanisms in discontinuous Galerkin finite element methods

F. Brezzi; B. Cockburn; L. D. Marini; E. Süli

doi:10.1016/j.cma.2005.06.015

Stabilization mechanisms in discontinuous Galerkin finite element methods

F. Brezzi
, B. Cockburn
, L. D. Marini
, E. Süli

School of Mathematics

Research output: Contribution to journal › Article › peer-review

112 Scopus citations

Abstract

In this paper we propose a new general framework for the construction and the analysis of discontinuous Galerkin (DG) methods which reveals a basic mechanism, responsible for certain distinctive stability properties of DG methods. We show that this mechanism is common to apparently unrelated stabilizations, including jump penalty, upwinding, and Hughes-Franca type residual-based stabilizations.

Original language	English (US)
Pages (from-to)	3293-3310
Number of pages	18
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	195
Issue number	25-28
DOIs	https://doi.org/10.1016/j.cma.2005.06.015
State	Published - May 1 2006

Keywords

Discontinuous Galerkin methods
Stabilization mechanisms

Publisher link

10.1016/j.cma.2005.06.015

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abstract = "In this paper we propose a new general framework for the construction and the analysis of discontinuous Galerkin (DG) methods which reveals a basic mechanism, responsible for certain distinctive stability properties of DG methods. We show that this mechanism is common to apparently unrelated stabilizations, including jump penalty, upwinding, and Hughes-Franca type residual-based stabilizations.",

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AU - Brezzi, F.

AU - Cockburn, B.

AU - Marini, L. D.

AU - Süli, E.

PY - 2006/5/1

Y1 - 2006/5/1

N2 - In this paper we propose a new general framework for the construction and the analysis of discontinuous Galerkin (DG) methods which reveals a basic mechanism, responsible for certain distinctive stability properties of DG methods. We show that this mechanism is common to apparently unrelated stabilizations, including jump penalty, upwinding, and Hughes-Franca type residual-based stabilizations.

AB - In this paper we propose a new general framework for the construction and the analysis of discontinuous Galerkin (DG) methods which reveals a basic mechanism, responsible for certain distinctive stability properties of DG methods. We show that this mechanism is common to apparently unrelated stabilizations, including jump penalty, upwinding, and Hughes-Franca type residual-based stabilizations.

KW - Discontinuous Galerkin methods

KW - Stabilization mechanisms

UR - https://www.scopus.com/pages/publications/33645924724

UR - https://www.scopus.com/pages/publications/33645924724#tab=citedBy

U2 - 10.1016/j.cma.2005.06.015

DO - 10.1016/j.cma.2005.06.015

M3 - Article

AN - SCOPUS:33645924724

SN - 0045-7825

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SP - 3293

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 25-28

ER -

Stabilization mechanisms in discontinuous Galerkin finite element methods

Abstract

Keywords

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