On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics

Details On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics On a nonlinear partial differential algebraic system arising in technical textile industry: Analysis and numerics

2012-03-16

arxiv.org/abs/1203.3692v1

Mathematics

Numerical Analysis

Scientific paper

In this paper a length-conserving numerical scheme for a nonlinear fourth order system of partial differential algebraic equations arising in technical textile industry is studied. Applying a semidiscretization in time, the resulting sequence of nonlinear elliptic systems with algebraic constraint 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 performed by projected gradient methods on finite element spaces which determine the computational effort and approximation quality of the algorithm. Simulation results are presented and discussed in view of the application of an elastic inextensible fiber motion.

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