Interfaces and Free Boundaries


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Volume 8, Issue 1, 2006, pp. 21–46
DOI: 10.4171/IFB/134

Published online: 2006-03-31

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

Klaus Deckelnick[1] and Gerhard Dziuk[2]

(1) Otto-von-Guericke-Universit├Ąt Magdeburg, Germany
(2) Universit├Ąt Freiburg, Germany

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.

Keywords: Willmore flow, fourth order parabolic problem, finite element, mixed method, error estimates

Deckelnick Klaus, Dziuk Gerhard: Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound. 8 (2006), 21-46. doi: 10.4171/IFB/134