Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh
This paper deals with a singularly perturbed one-dimensional boundary value problem. A standard, centered difference or finite element method on a piecewise equidistant mesh is considered. The author transforms the obtained equations so that the new equations have a monotonicity property and proves pointwise convergence, uniform in the perturbation parameter \(\varepsilon\) of second-order with respect to the number of nodes \(N\) on the coarse mesh, while the convergence is of order \(O(N^{-2}\ln^2 N)\) on the fine mesh. Some numerical results are presented.
scientific article; zbMATH DE number 1399550