Supraconvergence of a class of moving grid methods for solving a nonlinear problem Original Research Article

In this paper we generalize some previous results concerning moving grid methods for solving a second order linear initial/boundary value problem. Beginning with a generalization of some stability results obtained by Grigorieff, we proceed to a convergence study of a class of moving grid discretizations for solving a nonlinear evolution problem. As a particular case, the supraconvergence phenomenon of the method of lines can be observed. Finally, we present a relationship between the considered regridding method and the regridding criteria described in the literature and based on the equidistribution of some monitor function depending on the solution.