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Mixed methods for the approximation of liquid crystal flows. (English) Zbl 1032.76035
Summary: The numerical solution of the flow of a liquid crystal governed by Ericksen-Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve \(H^2(\Omega)\) norms of director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements, and establish convergence of the method.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A15 Liquid crystals
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
82D30 Statistical mechanical studies of random media, disordered materials (including liquid crystals and spin glasses)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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