Phase-field approximations of the Willmore functional and flow

@article{Bretin2015PhasefieldAO,
  title={Phase-field approximations of the Willmore functional and flow},
  author={E. Bretin and S. Masnou and {\'E}. Oudet},
  journal={Numerische Mathematik},
  year={2015},
  volume={131},
  pages={115-171}
}
We discuss in this paper phase-field approximations of the Willmore functional and the associated $${\mathrm L}^{2}$$L2-flow. After recollecting known results on the approximation of the Willmore energy and its $${\mathrm L}^{1}$$L1 relaxation, we derive the expression of the flows associated with various approximations, and we show their behavior by formal arguments based on matched asymptotic expansions. We introduce an accurate numerical scheme, whose local convergence is proved, to describe… Expand
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