Local discontinuous Galerkin schemes for a nonlinear variational wave equation modelling liquid crystals

Abstract

We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Discontinuous Galerkin schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Numerical experiments illustrating the stability and efficiency of the schemes are presented. An interesting feature of these schemes is their ability to approximate two distinct weak solutions of the underlying system.