연세대학교 계산과학공학

Time: 1:30-2:30 PM, Tuesday, November 5
Title:  Lower energy bounds in the Landau-de Gennes model for nematic liquid crystals
Abstract:
The mathematics and simulation of new materials is one of the challenges
in semilinear partial differential equations with a surprisingly complicated energy
landscape.  Pierre-Gilles de Gennes received the Nobel Prize in physics in 1991 for methods
developed for studying order phenomena in simple systems that can be generalized to more
complex forms of matter, in particular to liquid crystals and polymers. The Landau-de Gennes
minimization problem in the focus of the presentation is a very simplified model in nematic
liquid crystals. It is a semi-linear energy minimization problem of the Ginzburg-Landau-type
for superconductors. The presentation introduces some mathematics and focuses on the
discretization by the nonconforming enhanced Crouzeix-Raviart finite element method. After
some global weak convergence results, the discretization is utilized for  the computation
of  guaranteed lower energy bounds.  Numerical results show convergence and comparisons also
for a conforming variant.