A simple scheme for the approximation of the elastic flow of inextensible curves (Q2856614)

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 semi-implicit scheme is unconditionally stable and convergent. The rate of the convergence is documented two numerical examles.