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On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick

M. Elliott, Charles and Fritz, Hans (2016) On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick. IMA Journal of Numerical Analysis, drw020.

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Other URL: http://doi.org/10.1093/imanum/drw020


Abstract

In this article we discuss novel numerical schemes for the computation of the curve shortening and mean curvature flows that are based on special reparametrizations. The main idea is to use special solutions to the harmonic map heat flow in order to reparametrize the equations of motion. This idea is widely known from the Ricci flow as the De Turck trick. By introducing a variable timescale for ...

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Item type:Article
Date:2016
Institutions:Mathematics
Identification Number:
ValueType
10.1093/imanum/drw020DOI
Keywords:GEOMETRIC EVOLUTION-EQUATIONS; PARAMETRIC APPROXIMATION; HARMONIC MAPS; PLANE-CURVES; SURFACES; curve shortening flow; mean curvature flow; harmonic map heat flow; DeTurck trick; parametric finite elements; error estimates; tangential redistributions; mesh properties
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Published
Refereed:Yes, this version has been refereed
Created at the University of Regensburg:Yes
Item ID:39115
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