Geodesic
Error estimates for a semi-implicit fully discrete finite element scheme for the mean curvature flow of graphs
Klaus Deckelnick1 ; Gerhard Dziuk2
1Otto-von-Guericke-Universität Magdeburg, Germany
2Universität Freiburg, Germany
Interfaces and free boundaries, Tome 2 (2000) no. 4, pp. 341-359

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DOI

The efficient numerical simulation of the curvature-driven motion of interfaces is an important tool in several free- boundary problems. We treat the case of an interface which is given as a graph. The highly non-linear problem is discretized in space by piecewise linear finite elements. Although the problem is not in divergence form it can be written in a variational form which allows the use of the modern adaptive techniques of finite elements. The time discretization is carried out in a semi-implicit way such that in every time step a linear system with symmetric positive matrix has to be solved. Optimal error estimates are proved for the fully discrete problem under the assumption that the time-step size is bounded by the spatial grid size.
DOI : 10.4171/ifb/24
Classification : 46-XX, 60-XX
Mots-clés : finite element scheme, mean curvature flow

Klaus Deckelnick  1   ; Gerhard Dziuk  2

1 Otto-von-Guericke-Universität Magdeburg, Germany
2 Universität Freiburg, Germany 
Klaus Deckelnick; Gerhard Dziuk. Error estimates for a semi-implicit fully discrete finite element scheme for the mean curvature flow of graphs. Interfaces and free boundaries, Tome 2 (2000) no. 4, pp. 341-359. doi: 10.4171/ifb/24
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