A parametric finite element method for fourth order geometric evolution equations

@article{Barrett2007APF,
  title={A parametric finite element method for fourth order geometric evolution equations},
  author={John W. Barrett and Harald Garcke and Robert N{\"u}rnberg},
  journal={J. Comput. Physics},
  year={2007},
  volume={222},
  pages={441-467}
}
We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points. We… CONTINUE READING

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