A simple scheme for the approximation of the elastic flow of inextensible curves

Bartels, Sören
October 2013
IMA Journal of Numerical Analysis;Oct2013, Vol. 33 Issue 4, p1115
Academic Journal
A numerical scheme for the approximation of the elastic flow of inextensible curves is devised and convergence of approximations to exact solutions of the nonlinear time-dependent partial differential equation is proved. The nonlinear, pointwise constraint of local length preservation is linearized about a previous solution in each time step which leads to a sequence of linear saddle-point problems. The spatial discretization is based on piecewise Bézier curves and the resulting semiimplicit scheme is unconditionally stable and convergent.


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