Stability of Moving Mesh Systems of Partial Differential Equations

Moving mesh methods based on the equidistribution principle (EP) are studied from the viewpoint of stability of the moving mesh system of differential equations. For fine spatial grids, the moving mesh system inherits the stability of the original discretized partial differential equation (PDE). Unfortunately, for some PDEs the moving mesh methods require so many spatial grid points that they no longer appear to be practical. Failures and successes of the moving mesh method applied to three reaction-diffusion problems are explained via an analysis of the stability and accuracy of the moving mesh PDE.