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2013-04

A C1-finite element method for the Willmore flow of two-dimensional graphs

by Deckelnick, K., Katz, J., Schieweck, F..


Series: 2013-04, Preprints

MSC:
65M15 Error bounds
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

Abstract:
We consider the Willmore flow of two-dimensional graphs subject to Dirichlet boundary conditions. The corresponding evolution is described by a highly nonlinear parabolic PDE of fourth order for the height function. Based on a suitable weak form of the equation we derive a semidiscrete scheme which uses C1-finite elements and interpolates the Dirichlet boundary conditions. We prove quasioptimal error bounds in Sobolev norms for the solution and its time derivative and present results of test calculations.

Keywords:
Willmore flow, Dirichlet boundary conditions, C1-finite elements, error estimates