Geodesic
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
John W. Barrett1 ; Harald Garcke2 ; Robert Nürnberg1
1Imperial College London, United Kingdom
2Universität Regensburg, Germany
Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 187-234

Voir la notice de l'article provenant de la source EMS Press

DOI

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.
DOI : 10.4171/ifb/232
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Surface cluster, mean curvature flow, surface diffusion, soap bubbles, triple junction lines, parametric finite elements, anisotropy, tangential movement

John W. Barrett  1   ; Harald Garcke  2   ; Robert Nürnberg  1

1 Imperial College London, United Kingdom
2 Universität Regensburg, Germany 
John W. Barrett; Harald Garcke; Robert Nürnberg. Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies. Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 187-234. doi: 10.4171/ifb/232
@article{10_4171_ifb_232,
     author = {John W. Barrett and Harald Garcke and Robert N\"urnberg},
     title = {Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies},
     journal = {Interfaces and free boundaries},
     pages = {187--234},
     year = {2010},
     volume = {12},
     number = {2},
     doi = {10.4171/ifb/232},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/232/}
}
TY  - JOUR
AU  - John W. Barrett
AU  - Harald Garcke
AU  - Robert Nürnberg
TI  - Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
JO  - Interfaces and free boundaries
PY  - 2010
SP  - 187
EP  - 234
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/232/
DO  - 10.4171/ifb/232
ID  - 10_4171_ifb_232
ER  - 
%0 Journal Article
%A John W. Barrett
%A Harald Garcke
%A Robert Nürnberg
%T Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
%J Interfaces and free boundaries
%D 2010
%P 187-234
%V 12
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/232/
%R 10.4171/ifb/232
%F 10_4171_ifb_232

Cité par Sources :