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Error estimates for the Willmore flow of graphs

by Deckelnick, K., Dziuk, G..

Series: 2004-28, Preprints

65M15 Error bounds
35K55 Nonlinear parabolic equations
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

The evolution of two-dimensional graphs under Willmore flow
is approximated by a finite element method. The highly
nonlinear 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.

Willmore flow, finite elements, mixed method, error estimates