OPTIMAL ORDER L-2 ERROR ESTIMATE OF SDFEM ON SHISHKIN TRIANGULAR MESHES FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS

摘要

In this paper, we provide a convergence analysis for a streamline diffusion finite element method (SDFEM) for the singularly perturbed convection-diffusion equation on a Shishkin triangular mesh. The main result is to show that the SDFEM solution on the triangular mesh has the optimal order L-2 accuracy. The argument relies on a series of novel integral inequalities, which give the delicate estimations for the error terms related to the convection. Numerical experiments illustrate the proved results.