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

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...

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Bibliographic Details
Published in:arXiv.org 2015-03
Main Authors: Grothaus, Martin, Marheineke, Nicole
Format: Article
Language:English
Subjects:
Algebra
Computer simulation
Differential equations
Discretization
Finite element method
Hilbert space
Nonlinear systems
Optimization
Textile industry
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1203.3692