Edge stabilization for Galerkin approximations of convection–diffusion–reaction problems

In this paper we recall a stabilization technique for finite element methods for convection–diffusion–reaction equations, originally proposed by Douglas and Dupont [Computing Methods in Applied Sciences, Springer-Verlag, Berlin, 1976]. The method uses least square stabilization of the gradient jumps...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2004-01, Vol.193 (15), p.1437-1453
Main Authors: Burman, Erik, Hansbo, Peter
Format: Article
Language:English
Subjects:
Finite element
Interior penalty
Stabilized methods
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Summary:In this paper we recall a stabilization technique for finite element methods for convection–diffusion–reaction equations, originally proposed by Douglas and Dupont [Computing Methods in Applied Sciences, Springer-Verlag, Berlin, 1976]. The method uses least square stabilization of the gradient jumps a across element boundaries. We prove that the method is stable in the hyperbolic limit and prove optimal a priori error estimates. We address the question of monotonicity of discrete solutions and present some numerical examples illustrating the theoretical results.
ISSN:0045-7825
1879-2138
1879-2138
DOI:10.1016/j.cma.2003.12.032