SPECIAL MESHES FOR FINITE-DIFFERENCE APPROXIMATIONS TO AN ADVECTION-DIFFUSION EQUATION WITH PARABOLIC LAYERS

In this paper a model problem for fluid flow at high Reynolds number i s era mined, Parabolic boundary layers are present because part of the boundary of the domain is a characteristic of the reduced differentia l equation. For such problems it is shown, by numerical example, that upwind finite difference schemes on uniform meshes are not epsilon-uni formly convergent in the discrete L infinity norm, where epsilon is th e singular perturbation parameter. A discrete L infinity epsilon-unifo rmly convergent method is constructed for a singularly perturbed ellip tic equation, whose solution contains parabolic boundary layers for sm all values of the singular perturbation parameter epsilon. This method makes use of a special piecewise uniform mesh. Numerical results are given that validate the theoretical results, obtained earlier by the l ast author, for such special mesh methods. (C) 1995 Academic Press, In c.