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A fully discrete numerical scheme for weighted mean curvature flow

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Summary.

We analyze a fully discrete numerical scheme approximating the evolution of n–dimensional graphs under anisotropic mean curvature. The highly nonlinear problem is discretized by piecewise linear finite elements in space and semi–implicitly in time. The scheme is unconditionally stable und we obtain optimal error estimates in natural norms. We also present numerical examples which confirm our theoretical results.

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Authors and Affiliations

  1. Centre for Mathematical Analysis and Its Applications, School of Mathematical Sciences, University of Sussex, Falmer Brighton BN1 9QH, UK , , , , , , GB

    Klaus Deckelnick

  2. Institut für Angewandte Mathematik, Hermann–Herder–Strasse 10, 79104 Freiburg i. Br., Germany , , , , , , DE

    Gerhard Dziuk

Authors
  1. Klaus Deckelnick
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  2. Gerhard Dziuk
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Received October 2, 2000 / Published online July 25, 2001

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Deckelnick, K., Dziuk, G. A fully discrete numerical scheme for weighted mean curvature flow. Numer. Math. 91, 423–452 (2002). https://doi.org/10.1007/s002110100322

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  • DOI: https://doi.org/10.1007/s002110100322

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