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.
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Gerhard Dziuk, Klaus Deckelnick, Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound. 8 (2006), no. 1, pp. 21–46DOI 10.4171/IFB/134