Mixed Methods for the Approximation of Liquid Crystal Flows
Department of Mathematics, Pennsylvania State,
University, University Park, PA 18601, USA.
2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
Revised: 7 January 2002
The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve H2(Ω) norms of the 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.
Mathematics Subject Classification: 65M60 / 76A15
Key words: Liquid Crystals / Mixed Finite Element Approximation / Convergence.
© EDP Sciences, SMAI, 2002