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A singularly perturbed convection-diffusion problem, with a discontinuous convection coefficient and a singular perturbation parameter ε, is examined. Due to the discontinuity an interior layer appears in the solution. A finite difference method is constructed for solving this problem, which generates ε-uniformly convergent numerical approximations to the solution. The method uses a piecewise uniform mesh, which is fitted to the interior layer, and the standard upwind finite difference operator on this mesh. The main theoretical result is the ε-uniform convergence in the global maximum norm of the approximations generated by this finite difference method. Numerical results are presented, which are in agreement with the theoretical results.

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SUMMARYWe consider the classical problem of a two-dimensional laminar jet of incompressible uid owing into a stationary medium of the same uid. The equations of motion are the same as the boundary layer equations for ow past an inÿnite at plate, but with di erent boundary conditions. Numerical experiments show that, using appropriate piecewise-uniform meshes, numerical solutions together with their scaled discrete derivatives are obtained which are parameter (i.e., viscosity ) robust with respect to both the number of mesh nodes and the number of iterations required for convergence. While the method employed is non-conservative, we show with the aid of numerical experiments that the loss in conservation of momentum is minimal.