Elsevier

Applied Mathematics Letters

Volume 22, Issue 9, September 2009, Pages 1418-1424
Applied Mathematics Letters

A posteriori error estimates for subgrid viscosity stabilized approximations of convection–diffusion equations

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Abstract

We derive a posteriori error estimates for subgrid viscosity stabilized finite element approximations of convection–diffusion equations in the high Péclet number regime. Two estimators are analyzed: an asymptotically robust one and a fully robust one with respect to the Péclet number. Numerical results on test cases with boundary layers or internal layers show that the asymptotically robust estimator can be used to construct adaptive meshes.

Keywords

Finite elements
A posteriori error estimates
Subgrid viscosity
Advection–diffusion
High Péclet number regime

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This work was partly supported by the Volkswagen Foundation through Grant number I/79315 and by the French-Moroccan Project A.I number M.A/05/115. Partial support of the Groupement MoMaS (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN) is also gratefully acknowledged.