Error analysis of a finite element method for the Willmore flow of graphs
Klaus Deckelnick, Gerhard Dziuk · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2006
The evolution of two-dimensional graphs under Willmore flow is approximated by a continuousin-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.