Convergence of a crystalline algorithm
for the heat equation in one dimension
and for the motion of a graph
by weighted curvature |
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Authors: | Pedro Martins Gir\ao Robert V Kohn |
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Institution: | (1) Courant Institute, 251 Mercer Street, New York, NY 10012, USA , US |
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Abstract: | Summary.
Motion by (weighted) mean curvature is a geometric evolution law for
surfaces, representing steepest descent with respect to (an)isotropic
surface energy. It has been proposed that this motion could
be computed by solving the analogous evolution law using a
``crystalline' approximation to the surface energy. We present the
first convergence analysis for a numerical scheme of this type. Our
treatment is restricted to one dimensional surfaces (curves in the
plane) which are graphs. In this context, the scheme amounts to a new
algorithm for solving quasilinear parabolic equations in one space
dimension.
Received January 28, 1993 |
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Keywords: | Mathematics Subject Classification (1991): 65M12 73B30 35K20 |
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