On the approximation of the curve shortening flow. (English) Zbl 0830.65096
Bandle, C. (ed.) et al., Calculus of variations, applications and computations. Proceedings of the 2nd European conference on elliptic parabolic problems, Mont-à-Mousson, June 1994. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 326, 100-108 (1995).
This paper proposes a numerical scheme for the curve shortening flow in possibly higher codimension and proves convergence for a spatial discretization if the continuous problem has a smooth solution on some time interval. Numerical computations show that the numerical algorithm will continue past singularities although there is no convergence proof.
For the entire collection see [Zbl 0817.00011].
For the entire collection see [Zbl 0817.00011].
Reviewer: Q.Duan (Lafayette)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
