Quasi-optimal error estimate for the approximation of the elastic flow of inextensible curves

Abstract

A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint. Further a fully discrete time-stepping scheme that incorporates this constraint is proposed and unconditional stability and convergence of the discrete scheme are proved. Finally some numerical simulations are used to verify the obtained results experimentally.