We present a variational formulation of combined motion by minus the Laplacian of curvature and mean curvature flow, as well as related flows. The proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the equidistribution of mesh points and, if applicable, area conservation. © 2007 Society for Industrial and Applied Mathematics.

On the variational approximation of combined second and fourth order geometric evolution equations / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 29:3(2007), pp. 1006-1041. [10.1137/060653974]

On the variational approximation of combined second and fourth order geometric evolution equations

Nürnberg R.
2007

Abstract

We present a variational formulation of combined motion by minus the Laplacian of curvature and mean curvature flow, as well as related flows. The proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the equidistribution of mesh points and, if applicable, area conservation. © 2007 Society for Industrial and Applied Mathematics.
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Barrett, J. W.; Garcke, H.; Nürnberg, R.
On the variational approximation of combined second and fourth order geometric evolution equations / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 29:3(2007), pp. 1006-1041. [10.1137/060653974]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/283389
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