Improved Scheme on Adapted Locally-Uniform Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Problem

摘要

For a Dirichlet problem for a singularly perturbed parabolic convection-diffusion equation with small parameter e multiplying the highest-order derivative, a finite difference scheme with improved accuracy is constructed that converges almost s-uniformly with order of the convergence rate close to 2 for fixed values of s. When constructing the scheme, monotone classical approximations of the differential equation on a priori adapted locally-uniform meshes are used. To improve accuracy of the scheme, the Richardson technique on embedded grids is applied.