On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics
arXiv:1203.3692 · doi:10.1093/imanum/drv056
Abstract
In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry. Applying a semi-discretization in time, the resulting sequence of nonlinear elliptic systems with the algebraic constraint for the local length preservation is reformulated as constrained optimization problems in a Hilbert space setting that admit a solution at each time level. Stability and convergence of the scheme are proved. The numerical realization is based on a finite element discretization in space. The simulation results confirm the analytically predicted properties of the scheme.
Abstract and introduction are partially rewritten. The numerical study in Section 4 is completely rewritten