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Variational Methods for Discontinuous Structures pp 7–18Cite as

The Crystalline Algorithm for Computing Motion by Curvature

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 25))

Abstract

Motion by (weighted) mean curvature is a geometric evolution law for surfaces, representing steepest descent with respect to (anisotropic) surface energy. The crystalline algorithm is a numerical method for computing this motion. The main idea of this method is to solve the analogous evolution law for a crystalline surface energy which approximates the underlying smooth one. We have recently explored the nature of this method, demonstrating its convergence in some simple special cases. This paper summarizes our results.

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Author information

Authors and Affiliations

  1. Instituto Superior Tecnico, Av. Rovisco Pais, Lisboa, Portugal

    Pedro Martins Girão

  2. Courant Institute, New York University, New York, NY, 10012, USA

    Robert V. Kohn

Authors
  1. Pedro Martins Girão
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  2. Robert V. Kohn
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Pzza. Leonardo da Vinci, 32, I-20133, Milano, Italy

    Raul Serapioni  & Franco Tomarelli  & 

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Girão, P.M., Kohn, R.V. (1996). The Crystalline Algorithm for Computing Motion by Curvature. In: Serapioni, R., Tomarelli, F. (eds) Variational Methods for Discontinuous Structures. Progress in Nonlinear Differential Equations and Their Applications, vol 25. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9244-5_2

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  • DOI: https://doi.org/10.1007/978-3-0348-9244-5_2

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9959-8

  • Online ISBN: 978-3-0348-9244-5

  • eBook Packages: Springer Book Archive

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