A streamline diffusion finite element method on a shishkin mesh for a convection-diffusion problem |
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Authors: | Martin Stynes |
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Institution: | 1. Department of Mathematics, University College, Cork, Ireland
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Abstract: | We consider a model time-dependent convection-diffusion problem, whose solution may exhibit interior and boundary layers. The standard streamline diffusion scheme, with piecewise linear elements on a uniform mesh, will converge only at points that are not close to any layer. We replace the uniform mesh by a special piecewise uniform mesh that is chosen a priori and resolves part of any outflow boundary layer. The resulting method is convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 away from layers and almost order 3/4 inside the boundary layer. |
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