Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
The aim of this paper is to analyse a fully discrete finite element algorithm that approximates the mean curvature flow of graphs. The highly nonlinear problem is discretized in space by piecewise linear finite elements. The problem is written in a variational form which allows the use of the modern adaptive techniques of finite elements. The time discretization is carried out in a semi-implicit way such that in every time step a linear system with symmetric positive matrix has to be solved. Optimal error estimates are proved for the fully discrete problem under the assumption that the time-step size is bounded by the spatial grid size.
scientific article; zbMATH DE number 1545559