A finite difference analysis of a streamline diffusion method on a Shishkin mesh
The authors consider a singularly perturbed convection-diffusion boundary value problem whose solution has a single boundary layer. They use the streamline diffusion finite element method (SDFEM) to solve the problem. In fact, this SDFEM generates a finite differences scheme which satisfies a discrete maximum principle. This principle is the key fact in order to obtain the sharpest possible results. Moreover, the authors get to a relationship between the error in the numerical solution and a parameter of the Shishkin mesh. Some numerical experiments confirm the theoretical results.
convection-diffusion boundary value problem
streamline diffusion finite element method
scientific article; zbMATH DE number 1268413