Convergence Analysis of a Fully Discrete Energy-Stable Numerical Scheme for the Q-Tensor Flow of Liquid Crystals
Varun Gudibanda, Franziska Weber, Yukun Yue
Abstract
We present a fully discrete convergent finite difference scheme for the Q-tensor flow of liquid crystals based on the energy-stable semidiscrete scheme by Zhao et al. [Comput. Methods Appl. Mech. Engrg., 2017, pp. 803--825]. 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.
Topics & Concepts
MathematicsConvergence (economics)Tensor (intrinsic definition)Scheme (mathematics)Flow (mathematics)Mathematical analysisStability (learning theory)Balanced flowNumerical analysisApplied mathematicsEnergy functionalEnergy (signal processing)GeometryComputer scienceEconomic growthStatisticsMachine learningEconomicsAdvanced Numerical Methods in Computational MathematicsFluid Dynamics and Turbulent FlowsTheoretical and Computational Physics