Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities

Franz, Sebastian; Kellogg, R.; Stynes, Martin

doi:10.1090/S0025-5718-2011-02526-3

Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities
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by Sebastian Franz, R. Bruce Kellogg and Martin Stynes PDF

Math. Comp. 81 (2012), 661-685 Request permission

Abstract:

An error analysis of Galerkin and streamline diffusion finite element methods for the numerical solution of a singularly perturbed convection-diffusion problem is given. The problem domain is the unit square. The solution contains boundary layers and corner singularities. A tensor product Shishkin mesh is used, with piecewise bilinear trial functions. The error bounds are uniform in the singular perturbation parameter. Numerical results supporting the theory are given.

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