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In this paper, we analyze the streamline diffusion finite element method(SDFEM) for a model singularly perturbed convection-diffusion equation on aShishkin triangular mesh and hybrid meshes. Supercloseness property of$u^I-u^N$ is obtained, where $u^I$ is the interpolant of the solution $u$ and$u^N$ is the SDFEM's solution. The analysis depends on novel integralinequalities for the diffusion and convection parts in the bilinear form.Furthermore, analysis on hybrid meshes shows that bilinear elements should berecommended for the exponential layer, not for the characteristic layer.Finally, numerical experiments support these theoretical results.

Analysis of SDFEM on Shishkin triangular meshes and hybrid meshes for problems with characteristic layers