Convergence in L2 norm of the SDFEM on a Shishkin triangular mesh for problems with characteristic layers

In this paper, we analyze a streamline diffusion finite element method (SDFEM) on a Shishkin triangular mesh, which is applied to a model singularly perturbed convection-diffusion problem. The main result is to show the SDFEM solution on the triangular mesh possesses the optimal convergence order in the L2 norm provided that the diffusion coefficient is sufficiently small compared with the mesh size. Numerical experiments illustrate the theoretical result.