ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Mixed Methods for the Approximation of Liquid Crystal Flows

Liu, Chuna1 and Walkington, Noel J.a2

a1 Department of Mathematics, Pennsylvania State, University, University Park, PA 18601, USA.

a2 Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

Abstract

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.

(Received December 11 2000)

(Revised January 7 2002)

(Online publication May 15 2002)

Key Words:

  • Liquid Crystals;
  • Mixed Finite Element Approximation;
  • Convergence.

Mathematics Subject Classification:

  • 65M60;
  • 76A15
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