On the Convergence of the Dirichlet Grid Problem with a Singularity for a Singularly Perturbed Convection-Diffusion Equation

摘要

The Dirichlet problem for a singulary perturbed convection-diffusion equation in a rectangle when a discontinuity at the flow exit the first derivative of the boundary condition gives rise to an inner layer for the solution. On piecewise-uniform Shishkin grids that condense near regular and characteristic layers, the solution obtained using the classical five-point difference scheme with a directed difference is shown to converge with respect to the small parameter to solve the original problem in the grid norm almost with the first order. This theoretical result is confirmed via numerical analysis.