Superconvergence Analysis of Galerkin FEM and SDFEM for Elliptic Problems with Characteristic Layers

We analyse the superconvergence properties of the Galerkin FEM and of the streamline-diffusion finite element method (SDFEM) using bilinear functions in the case of elliptic problems with characteristic layers. To resolve the layers we use appropriate Shishkin meshes.

For the SDFEM we give an optimal choice for the streamline-diffusion parameter δ for maximal stability in the induced streamline-diffusion norm. In the characteristic layers we are able to show that δ can be chosen of order δ = Cε- N^–2 which is con.rmed by numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)