JournalsifbVol. 12, No. 4pp. 551–574

Error analysis for the approximation of axisymmetric Willmore flow by <i>C</i><sup>1</sup>-finite elements

  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
  • Friedhelm Schieweck

    Otto-von-Guericke-Universität Magdeburg, Germany
Error analysis for the approximation of axisymmetric Willmore flow by <i>C</i><sup>1</sup>-finite elements cover
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Abstract

We consider the Willmore flow of axially symmetric surfaces subject to Dirichlet boundary conditions. The corresponding evolution is described by a nonlinear parabolic PDE of fourth order for the radius function. A suitable weak form of the equation, which is based on the first variation of the Willmore energy, leads to a semidiscrete scheme, in which we employ piecewise cubic _C_1-finite elements for the one-dimensional approximation in space.We prove optimal error bounds in Sobolev norms for the solution and its time derivative and present numerical test examples.

Cite this article

Klaus Deckelnick, Friedhelm Schieweck, Error analysis for the approximation of axisymmetric Willmore flow by <i>C</i><sup>1</sup>-finite elements. Interfaces Free Bound. 12 (2010), no. 4, pp. 551–574

DOI 10.4171/IFB/245