Uniform pointwise convergence of an upwind finite volume method on layer-adapted meshes

摘要

A singularly perturbed convection-diffusion problem is considered. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We establish first-order global pointwise convergence no matter how small the perturbation parameter. We show both theoretically and experimentally that certain choices of the stabilization parameter are particularly favourable. Numerical experiments support the theoretical results. [References: 26]