On simple moving grid methods for one-dimensional evolutionary partial differential equations (Q1103347)

Two moving grid algorithms for the numerical integration of evolutionary one-dimensional PDE, based on a Galerkin approach: the Bonnerot-Jamet discretization technique and on discretization of the Lagrangian form of the time derivative, are considered. Both algorithms are successful in following and resolving very sharp profiles without coupling the grid selection and the computation of the solution, working better in this respect than a scheme of interpolatory kind. The disadvantage is that due to the intrinsic coupling of the computations of the grid and the solution, the size of the system of nonlinear equations to be solved at each step, becomes larger. A discussion is made how to avoid the IEL inaccuracy problems and BJCN instability.