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Error expansion for an upwind scheme applied to a two-dimensional convection-diffusion problem. (English) Zbl 1055.65119
This paper is concerned with a singularly perturbed convection-diffusion problem in a rectangular domain. The problem is solved using a first-order upwind finite difference scheme on a tensor-product piecewise-uniform Shishkin mesh with $$O(N)$$ mesh points in each coordinate directions. An error analysis is discussed and numerical examples are proposed.

##### MSC:
 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35B25 Singular perturbations in context of PDEs 65N06 Finite difference methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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