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Edge stabilisation for Galerkin approximations of convection-diffusion-reaction problems

journal contribution
posted on 2023-06-08, 10:08 authored by Erik Burman, Peter Hansbo
n this paper we recall a stabilization technique for finite element methods for convection-diffusion-reaction equations, originally proposed by J. Douglas, Jr. and T. Dupont [in Computing methods in applied sciences (Second Internat. Sympos., Versailles, 1975), 207--216, Lecture Notes in Phys., 58, Springer, Berlin, 1976; MR0440955 (55 \\#13823)]. The method uses least square stabilization of the gradient jumps 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.

History

Publication status

  • Published

Journal

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

Volume

193

Page range

1437-1453

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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