Supraconvergence of a class of moving grid methods for solving a nonlinear problem (Q1917474)

The author proves a so-called supraconvergence result for finite difference schemes on nonuniform spatial grids discretizing quasilinear parabolic equations. By supraconvergence one denotes the phenomenon that the approximate solutions are second-order in the spatial grid size convergent although the scheme has a first-order truncation error only. The grid is assumed to vary not too strongly with respect to time which is the case if familiar monitoring criteria for the grid distribution are used. The proof of the result is based on an a priori estimate for nonlinear boundary value problems of ordinary differential equations which generalizes Spijker-norm stability inequalities obtained by the author for linear equations.