We present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in ℝd, d ≥ 2. This new formulation leads to an unconditionally stable, fully discrete, parametric finite element approximation in the case d = 2 or 3. The resulting scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments for d = 3, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion. © 2008 Springer-Verlag.

A variational formulation of anisotropic geometric evolution equations in higher dimensions / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 109:1(2008), pp. 1-44. [10.1007/s00211-007-0135-5]

A variational formulation of anisotropic geometric evolution equations in higher dimensions

Nürnberg R.
2008

Abstract

We present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in ℝd, d ≥ 2. This new formulation leads to an unconditionally stable, fully discrete, parametric finite element approximation in the case d = 2 or 3. The resulting scheme has very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments for d = 3, including regularized crystalline mean curvature flow and regularized crystalline surface diffusion. © 2008 Springer-Verlag.
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Barrett, J. W.; Garcke, H.; Nürnberg, R.
A variational formulation of anisotropic geometric evolution equations in higher dimensions / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 109:1(2008), pp. 1-44. [10.1007/s00211-007-0135-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/283447
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