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A numerical scheme for moving boundary problems that are gradient flows for the area functional

Published online by Cambridge University Press:  01 February 2000

UWE F. MAYER
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

Abstract

Many moving boundary problems that are driven in some way by the curvature of the free boundary are gradient flows for the area of the moving interface. Examples are the Mullins–Sekerka flow, the Hele-Shaw flow, flow by mean curvature, and flow by averaged mean curvature. The gradient flow structure suggests an implicit finite differences approach to compute numerical solutions. The proposed numerical scheme will allow us to treat such free boundary problems in both IR2 and IR3. The advantage of such an approach is the re-usability of much of the setup for all of the different problems. As an example of the method, we compute solutions to the averaged mean curvature flow that exhibit the formation of a singularity.

Type
Research Article
Copyright
2000 Cambridge University Press

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