07-38
Error analysis for the elastic flow of parametrized curves
Preprint series: 07-38, Preprints
- MSC:
- 35K55 Nonlinear PDE of parabolic type
- 65M15 Error bounds
- 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Abstract: 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.
Keywords: elastic flow, finite elements, error estimates
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