JournalsifbVol. 8, No. 1pp. 21–46

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

  • Gerhard Dziuk

    Universität Freiburg, Germany
  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
Error analysis of a finite element method for the Willmore flow of graphs cover
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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.

Cite this article

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. 21–46

DOI 10.4171/IFB/134