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Continuous interior penalty method on a Shishkin mesh for convection–diffusion problems with characteristic boundary layers

✍ Scribed by S. Franz

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
239 KB
Volume
197
Category
Article
ISSN
0045-7825

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✦ Synopsis

The continuous interior penalty (CIP) method for elliptic convection-diffusion problems with characteristic layers on a Shishkin mesh is analysed. The method penalises jumps of the normal derivative across interior edges. We show that it is of the same order of convergence as the streamline diffusion finite-element method and is superclose in the CIP norm induced by its bilinear form for the difference between the FEM solution and the bilinear nodal interpolant of the exact solution. Furthermore, we study numerically the behaviour of the method for different choices of the stabilisation parameter.

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