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Error analysis for the elastic flow of parametrized curves

by Deckelnick, K., Dziuk, G..

Series: 2007-38, Preprints

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

We analyze a semidiscrete numerical scheme for approximating
the evolution of parametric curves by elastic flow. The
fourth order equation is split into two coupled second order
problems, which are approximated by linear finite elements.
We prove error bounds for the resulting scheme and present
numerical test calculations that confirm our analysis.

elastic flow, finite elements, error estimates