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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 Hansbon 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.
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Publication status
- Published
Journal
Computer Methods in Applied Mechanics and EngineeringISSN
0045-7825External DOI
Volume
193Page range
1437-1453Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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