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Convergence of a finite element method for non-parametric mean curvature flow

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Summary.

Convergence for the spatial discretization by linear finite elements of the non-parametric mean curvature flow is proved under natural regularity assumptions on the continuous solution. Asymptotic convergence is also obtained for the time derivative which is proportional to mean curvature. An existence result for the continuous problem in adequate spaces is included.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Hermann-Herder-Str. 10, D-79104 Freiburg i.Br., Germany , , , , , , DE

    Klaus Deckelnick & Gerhard Dziuk

Authors
  1. Klaus Deckelnick
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  2. Gerhard Dziuk
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Received September 30, 1993

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Deckelnick, K., Dziuk, G. Convergence of a finite element method for non-parametric mean curvature flow . Numer. Math. 72, 197–222 (1995). https://doi.org/10.1007/s002110050166

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  • DOI: https://doi.org/10.1007/s002110050166