Geodesic
Error analysis for the approximation of axisymmetric Willmore flow by $C^1$-finite elements
Klaus Deckelnick1 ; Friedhelm Schieweck1
1Otto-von-Guericke-Universität Magdeburg, Germany
Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 551-574

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DOI

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 C1-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.
DOI : 10.4171/ifb/245
Classification : 35-XX, 65-XX, 00-XX
Mots-clés : Willmore flow; Dirichlet boundary conditions; finite elements; error estimates

Klaus Deckelnick  1   ; Friedhelm Schieweck  1

1 Otto-von-Guericke-Universität Magdeburg, Germany 
Klaus Deckelnick; Friedhelm Schieweck. Error analysis for the approximation of axisymmetric Willmore flow by $C^1$-finite elements. Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 551-574. doi: 10.4171/ifb/245
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/245/}
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