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Approximation of liquid crystal flows. (English) Zbl 1040.76036
The authors consider a simplified version of Ericksen-Leslie system modeling the flow of a liquid crystal. The system couples a Navier-Stokes type equation for the velocity and pressure of the fluid to an equation of Ginzburg-Landau type for the director field. Based on an appropriate weak form of the system, the authors introduce a discrete scheme using finite elements in space and the backward Euler method in time. Under suitable assumptions on the regularity of the solution, they obtain error estimates for velocity, pressure and director field. Finally, they present numerical examples which illustrate the behavior of liquid crystal flows in the presence of singularities.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A15 Liquid crystals
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