Stabilization of Galerkin Finite Element Approximations to Transient Convection-Diffusion Problems

Abstract

A postprocessing technique to improve Galerkin finite element approximations to linear evolutionary convection-reaction-diffusion equations is considered. A steady convection-reactiondiffusion problem with data based on the computed standard Galerkin approximation is solved at any fixed time. The postprocessing approximation is obtained using the SUPG method over the same Galerkin finite element space. Error bounds for the method are obtained in the convectiondominated regime. The numerical experiments we present show a substantial reduction of spurious oscillations achieved by means of this procedure.