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

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 @e, with a pointwise accuracy of almost order 7/4 away from the characteristic layers. Numerical experiments support these theoretical results.

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