A posteriori error analysis for the mean curvature flow of graphs

We study the equation describing the motion of a nonparametric surface according to its mean curvature flow. This is a nonlinear nonuniformly parabolic PDE that can be discretized in space via a finite element method. We conduct an aposteriori error analysis of the spatial discretization and derive upper bounds on the error in terms of computable estimators based on local residual indicators. The reliability of the estimators is illustrated with two numerical simulations, one of which treats the case of a singular solution.