CONVERGENCE OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR A DEGENERATE PARABOLIC SYSTEM MODELLING NEMATIC LIQUID CRYSTALS WITH VARIABLE DEGREE OF ORIENTATION
CONVERGENCE OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR A DEGENERATE PARABOLIC SYSTEM MODELLING NEMATIC LIQUID CRYSTALS WITH VARIABLE DEGREE OF ORIENTATION
复制标题
退化抛物线系统的全离散有限元方法的收敛性，用于模拟可变取向向列液晶
DOI：
10.1051/m2an:2006005
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Prohl
中科院分区：
文献类型：
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作者：
J. Barrett;Xiaobing H. Feng;A. Prohl
我们考虑一个简并抛物线系统，它模拟具有不同取向度的向列液晶的演化。该系统对 [Calderer 等人提出的系统稍作修改。 ，SIAM J.数学。肛门。 33 (2002) 1033–1047]，这是 [Ericksen, Arch. 33 (2002) 1033–1047] 中 Ericksen 一般连续统模型的特例。配给。机甲。肛门。 113（1991）97-120]。我们通过传递到正则化系统中的极限来证明弱解的全局存在性。此外，我们针对该正则化系统提出了一种实用的全离散有限元方法，并且当网格参数趋于零时，我们建立了该有限元近似对正则化系统解的（子序列）收敛性；以及当网格和正则化参数都接近零时原始简并抛物线系统的解。最后，还包括数值实验，显示了此类模型中线奇点/缺陷的形成、湮灭和演化。
We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer et al. , SIAM J. Math. Anal. 33 (2002) 1033–1047], which is a special case of Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal. 113 (1991) 97–120]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical fully discrete finite element method for this regularized system, and we establish the (subsequence) convergence of this finite element approximation to the solution of the regularized system as the mesh parameters tend to zero; and to a solution of the original degenerate parabolic system when the the mesh and regularization parameters all approach zero. Finally, numerical experiments are included which show the formation, annihilation and evolution of line singularities/defects in such models.