In this paper we consider the numerical approximation of phase field and sharp interface models for diffusion-induced grain boundary motion. The phase field model consists of a double-obstacle Allen-Cahn equation with a forcing obtained from the solution of a degenerate diffusion equation. On the other hand the sharp interface model consists of forced mean curvature flow coupled to a diffusion equation holding on the interface itself. Formal asymptotics yield the sharp interface model as the limit of the phase field equations as the width of the associated diffuse interface tends to zero. A finite-element approximation of the phase field model is presented and is shown to be convergent to a weak solution. Numerical simulations of both models are described and compared. It is shown that the two models are consistent.
Classification :
46-XX, 60-XX
Mots-clés :
Grain boundary motion, phase field mode, sharp interface, mean curvature flow, finite-element approximation
Affiliations des auteurs :
Klaus Deckelnick
1
;
Charles M. Elliott
2
;
Vanessa Styles
3
1
Otto-von-Guericke-Universität Magdeburg, Germany
2
University of Warwick, Coventry, UK
3
University of Sussex, Brighton, UK
Klaus Deckelnick; Charles M. Elliott; Vanessa Styles. Numerical diffusion-induced grain boundary motion. Interfaces and free boundaries, Tome 3 (2001) no. 4, pp. 393-414. doi: 10.4171/ifb/46
@article{10_4171_ifb_46,
author = {Klaus Deckelnick and Charles M. Elliott and Vanessa Styles},
title = {Numerical diffusion-induced grain boundary motion},
journal = {Interfaces and free boundaries},
pages = {393--414},
year = {2001},
volume = {3},
number = {4},
doi = {10.4171/ifb/46},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/46/}
}
TY - JOUR
AU - Klaus Deckelnick
AU - Charles M. Elliott
AU - Vanessa Styles
TI - Numerical diffusion-induced grain boundary motion
JO - Interfaces and free boundaries
PY - 2001
SP - 393
EP - 414
VL - 3
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/46/
DO - 10.4171/ifb/46
ID - 10_4171_ifb_46
ER -
%0 Journal Article
%A Klaus Deckelnick
%A Charles M. Elliott
%A Vanessa Styles
%T Numerical diffusion-induced grain boundary motion
%J Interfaces and free boundaries
%D 2001
%P 393-414
%V 3
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/46/
%R 10.4171/ifb/46
%F 10_4171_ifb_46
