We present a variational formulation for the evolution of surface clusters in R3 by mean curvature flow, surface diffusion and their anisotropic variants. We introduce the triple junction line conditions that are induced by the considered gradient flows, and present weak formulations of these flows. In addition, we consider the case where a subset of the boundaries of these clusters are constrained to lie on an external boundary. These formulations lead to unconditionally stable, fully discrete, parametric finite element approximations. The resulting schemes have very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments, including isotropic double, triple and quadruple bubbles, as well as clusters evolving under anisotropic mean curvature flow and anisotropic surface diffusion, including computations for regularized crystalline surface energy densities. © European Mathematical Society 2010.

Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 12:2(2010), pp. 187-234. [10.4171/IFB/232]

Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies

Nürnberg R.
2010-01-01

Abstract

We present a variational formulation for the evolution of surface clusters in R3 by mean curvature flow, surface diffusion and their anisotropic variants. We introduce the triple junction line conditions that are induced by the considered gradient flows, and present weak formulations of these flows. In addition, we consider the case where a subset of the boundaries of these clusters are constrained to lie on an external boundary. These formulations lead to unconditionally stable, fully discrete, parametric finite element approximations. The resulting schemes have very good properties with respect to the distribution of mesh points and, if applicable, volume conservation. This is demonstrated by several numerical experiments, including isotropic double, triple and quadruple bubbles, as well as clusters evolving under anisotropic mean curvature flow and anisotropic surface diffusion, including computations for regularized crystalline surface energy densities. © European Mathematical Society 2010.
2010
2
Barrett, J. W.; Garcke, H.; Nürnberg, R.
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies / Barrett, J. W.; Garcke, H.; Nürnberg, R.. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 12:2(2010), pp. 187-234. [10.4171/IFB/232]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/283495
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 30
  • ???jsp.display-item.citation.isi??? 27
social impact