Speaker
Description
We present a continuous and a discontinuous linear Finite Element method based on a predictor-corrector scheme for the numerical approximation of the Ericksen-Leslie equations, a model for nematic liquid crystal flow including the non-convex unit-sphere constraint. As predictor step we propose a linear semi-implicit Finite Element discretization which naturally offers a local orthogonality relation between the approximate director field and its time derivative. Afterwards an explicit discrete projection onto the unit-sphere constraint is applied without increasing the modeled energy. We compare the established method of using a discrete inner product usually referred to as mass-lumping for a globally continuous Finite Element discretization against a piecewise constant discontinuous Galerkin approach. Discrete Well-posedness results and energy laws are established. Conditional convergence of subsequences of the approximate solutions to energy-variational solutions of the Ericksen-Leslie equations is shown for a time-step restriction. Computational studies indicate the efficiency of the proposed linearization and the improved accuracy by including a projection step in the algorithm.
