Oberseminar Numerische Mathematik / Scientific Computing
Klaus Deckelnick
Otto-von-Guericke-Universität, Magdeburg
Error analysis for the approximation of axisymmetric Willmore flow by C1-finite elements
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 radial variable. 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. This is joint work with Friedhelm Schieweck (Magdeburg).
| Datum: | 17.05.10 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | 031 im Erdgeschoss |