How Accurate is the Streamline Diffusion
Finite Element Method?
Abstract: We investigate the optimal accuracy of the streamline diffusion finite element method applied to convection-dominated problems. For linear/bilinear elements the theoretical order of convergence given in the literature is either for quasi-uniform meshes or for some uniform meshes. The determination of the optimal order in general was an open problem. By studying a special type of meshes, it is shown that the streamline diffusion method may actually converge with any order within this range depending on the characterization of the meshes.
Keywords: Convection--diffusion problems, streamline diffusion finite element method, structured meshes, superconvergence
Received by editor(s): June 1, 1995
Additional Notes: This work was supported by the Deutsche Forschungsgemeinschaft, SFB 359, Universität Heidelberg, Germany.
Article copyright: © Copyright 1997 American Mathematical Society