Error analysis of a finite element method for the Willmore flow of graphs

Abstract

The evolution of two-dimensional graphs under Willmore flow is approximated by a continuous-in-time finite element method. The highly nonlinear fourth order problem is split into two coupled second order problems using height and a weighted mean curvature as variables. We prove a-priori error estimates for the resulting time-continuous scheme and present results of test calculations. © European Mathematical Society 2006.