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Computing solutions of convection-diffusion equations is an im- portant 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 Par- tial 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 stabiliza- tion parameter introduced in (Serghini Mounim, A stabilized finite element method for convection-diffusion problems, Numer. Methods Partial Differen- tial Eq. 28 (2012), 1916-1943) gives much better results than the standard Streamline upwind/Petrov-Galerkin (SUPG) one.

ON A STABILIZED FINITE ELEMENT METHOD WITH MESH ADAPTIVE PROCEDURE FOR CONVECTION--DIFFUSION PROBLEMS