Modelling, Analysis and Simulation On the convergence analysis of advection-diffusion schemes on non-uniform grids

Numerical schemes for advection-di usion problems are often used with non-uniform grids. Non-uniform grids are known to greatly complicate the convergence analysis and their use therefore is much less straightforward than for uniform grids. For example, it is possible that a scheme which is inconsistent at the level of the local truncation error truly converges with order two. The purpose of this paper is to contribute to the theory of spatial discretizations on non-uniform grids. We shall present spatial convergence results for a number of vertex and cell centered schemes for the linear 1D time-dependent advection-di usion problem. The focus hereby lies on the discrepancy between local and global order. 2000 Mathematics Subject Classi cation: 65M06, 65M12, 65M50, 65N06, 65N12, 65N50.