Finite differences - mesh drift and superconvergence

Speaker : Daniel R. Reese

Abstract : One of the difficulties in setting up higher order finite-difference schemes is the so-called mesh-drift instability. Such an instability leads to a decoupling of even and odd grid points, thereby leading to solution functions with a jigsaw pattern. Current ways of dealing with this defect include introducing artificial viscosity or applying a staggered grid approach. These remedies may unduly modify the solutions (especially in a non-dissipative problem), introduce supplementary free parameters, or or lead to complications when applying boundary conditions. We propose a new method, inspired from the staggered grid strategy, which removes this instability while bypassing the above difficulties. Furthermore, this approach lends itself to superconvergence, a process in which the accuracy of the finite differences is boosted by one order.