Convergence analysis of a fully discrete energy-stable numerical scheme for the Q-tensor flow of liquid crystals

12/01/2020

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by   Varun M. Gudibanda, et al.

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We present a fully discrete convergent finite difference scheme for the Q-tensor flow of liquid crystals based on the energy-stable semi-discrete scheme by Zhao, Yang, Gong, and Wang (Comput. Methods Appl. Mech. Engrg. 2017). We prove stability properties of the scheme and show convergence to weak solutions of the Q-tensor flow equations. We demonstrate the performance of the scheme in numerical simulations.