Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Stochastic dynamics for inextensible fibers in a spatially semidiscrete setting
:
Lindner, Felix; Marheinke, Nicole; Stroot, Holger; Vibe, Alexander; Wegener, Raimund  Stochastics and Dynamics 17 (2017), Nr.2, Art. 1750016, 29 S. ISSN: 02194937 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer ITWM () 
 stochastic elastic beam dynamics; stochastic differential algebraic equation; manifoldvalued stochastic differential equation; nonlinear constraint; global solution theory 
Abstract
We investigate a spatially discrete surrogate model for the dynamics of a slender, elastic, inextensible fiber in turbulent flows. Deduced from a continuous spacetime beam model for which no solution theory is available, it consists of a highdimensional second order stochastic differential equation in time with a nonlinear algebraic constraint and an associated Lagrange multiplier term. We establish a suitable framework for the rigorous formulation and analysis of the semidiscrete model and prove existence and uniqueness of a global strong solution. The proof is based on an explicit representation of the Lagrange multiplier and on the observation that the obtained explicit drift term in the equation satisfies a onesided linear growth condition on the constraint manifold. The theoretical analysis is complemented by numerical studies concerning the time discretization of our model. The performance of implicit Eulertype methods can be improved when using the explicit representation of the Lagrange multiplier to compute refined initial estimates for the Newton method applied in each time step.