Zeit: | Donnerstag, 21.01.1999, 09:00 Uhr |
Ort: | Reichenhainer Straße 70, B201 |
Vortragender: | Prof. L. Tobiska (Magdeburg) |
Thema: | Properties of the Streamline-Diffusion Finite Element Method on a Shishkin Mesh for Singularly Perturbed Elliptic Equations with Exponential Layers |
On the unit square, we consider a singularly perturbed convection-diffusion boundary value problem whose solution has exponential boundary layers along two sides of the square. We use the streamline-diffusion finite element method (SDFEM) with piecewise bilinear trial functions on a Shishkin mesh of O(N2) points and show that it is convergent, uniformly in the diffusion parameter , of order to its bilinear interpolant in the usual streamline-diffusion norm. As a corollary we prove that the method is convergent of order (again uniformly in ) in the local norm on the fine part of the mesh (i.e., inside the boundary layers). This local estimate within the layers can be improved to order , uniformly in , away from the corner layer. We present numerical results to support these results and to examine the effect of replacing bilinear trials with linear trials in the SDFEM. | |
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