How accurate is the streamline-diffusion FEM inside characteristic (boundary and interior) layers?
Two model two-dimensional singularly perturbed convectiondiffusion problems are considered whose solutions may have characteristic boundary and interior layers. They are solved numerically by the streamline-diffusion finite element method using piecewise linear or bilinear elements. We investigate how accurate the computed solution is in characteristic-layer regions if anisotropic layer-adapted meshes are used. It is shown that the streamline-diffusion formulation may, in the maximum norm, imply only first-order accuracy in characteristic-layer regions. Numerical experiments are presented that support our theoretical predictions.
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