ON A STABILIZED FINITE ELEMENT METHOD
WITH MESH ADAPTIVE PROCEDURE FOR
CONVECTION-DIFFUSION PROBLEMS
M. Farhloul1, A. Serghini Mounim2, A. Zine3
1Département de Mathématiques et de Statistique
Université de Moncton
Moncton, N.B., E1A 3E9, CANADA
2Department of Mathematics and Computer Science
Laurentian University
Sudbury, Ontario, P3E 2C6, CANADA
3Département de Mathématiques et Informatique
Université de Lyon
Institut Camille Jordan, CNRS-UMR5208
Ecole Centrale de Lyon, 36 av. Guy de Collongue
69134 Ecully Cedex, FRANCE
Abstract. Computing solutions of convection-diffusion equations is an important and challenging problem from the numerical point of view. We present in this work a numerical scheme to study this problem. The scheme combines a stabilized finite element method introduced in [Serghini Mounim, A stabilized finite element method for convection-diffusion problems, Mumer. Methods Partial Differential Eq 28: 1916-1943, 2012], with an adaptive mesh refinement procedure which is based on the residual a posteriori error estimators. It is worthwhile to point out that the numerical results indicate that the stabilization parameter introduced in [Serghini Mounim, A stabilized finite element method for convection-diffusion problems, Numer. Methods Partial Differential Eq. 28 (2012), 1916-1943] gives much better results than the standard Streamline upwind/Petrov-Galerkin (SUPG) one.
AMS Subject Classification: 65N30, 65N15, 65N50
Key Words and Phrases: convection-diffusion equations, streamline upwind/Petrov-Galerkin method, residual-free bubble method, residual a posteriori error estimates, adaptive mesh refinement


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DOI: 10.12732/ijam.v28i6.3

Volume: 28
Issue: 6
Year: 2015