Pointwise estimates of the SDFEM for convection–diffusion problems with characteristic layers

Abstract

A model singularly perturbed convection–diffusion problem in two space dimensions is considered. The problem is solved by a streamline diffusion finite element method (SDFEM) that uses piecewise bilinear finite elements on a Shishkin mesh. We prove that the method is convergent, independently of the diffusion parameter ε, with a pointwise accuracy of almost order 7/4 away from the characteristic layers. Numerical experiments support these theoretical results.