In:
Numerische Mathematik, Springer Science and Business Media LLC, Vol. 149, No. 2 ( 2021-10), p. 375-415
Abstract:
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open curves we propose natural boundary conditions that respect the appropriate gradient flow structure. Based on suitable weak formulations we introduce finite element approximations using piecewise linear elements. For some of the schemes a stability result can be shown. The derived schemes can be employed in very different contexts. For example, we apply the schemes to the Angenent metric in order to numerically compute rotationally symmetric self-shrinkers for the mean curvature flow. Furthermore, we utilise the schemes to compute geodesics that are relevant for optimal interface profiles in multi-component phase field models.
Type of Medium:
Online Resource
ISSN:
0029-599X
,
0945-3245
DOI:
10.1007/s00211-021-01231-6
Language:
English
Publisher:
Springer Science and Business Media LLC
Publication Date:
2021
detail.hit.zdb_id:
1364300-9
detail.hit.zdb_id:
3460-5
detail.hit.zdb_id:
2106413-1
SSG:
17,1
