Pointwise estimates of SDFEM on Shishkin triangular meshes for problems with characteristic layers

In this paper, we present pointwise estimates of the streamline diffusion finite element method (SDFEM) for conforming piecewise linears on Shishkin triangular meshes. The method is applied to a model singularly perturbed convection-diffusion problem with characteristic layers. Using a new variant of artificial crosswind diffusion, we prove that uniformly pointwise error bounds away from the layers are of order almost 7/4 (up to a logarithmic factor). In some cases, the convergence order is almost 15/8. Our analysis depends on discrete Green's functions and sharp estimates of the diffusion and convection parts in the bilinear form. Finally, numerical experiments support our theoretical results.