Pointwise error estimates of the bilinear SDFEM on Shishkin meshes

Abstract

AbstractA 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 11/8 outside and inside the boundary layers. Numerical experiments support these theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013