Uniform Convergence Analysis of an Upwind Finite-Difference Approximation of a Convection-Diffusion Boundary Value Problem on an Adaptive Grid.

Uniform convergence analysis of an upwind nite-diierence approximation of a convection-diiusion boundary value problem on an adaptive grid. We derive an-uniform error estimate for the rst-order upwind discretisation of a model convection-diiusion boundary value problem on a non-uniform grid. Here, is the small parameter multiplying the highest derivative term. The grid is suggested by the equidistribution of a power of the solution gradient. The use of equidistribution principles appears in many grid adaption schemes and our analysis indicates the convergence behaviour on such grids. Numerical results are given that connrm the-uniform convergence rate.