On convergence of an unconditional stable numerical scheme for Q-tensor flow based on invariant quardratization method

2022/10/02 by Yukun Yue, Yue, Yukun
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2210.00495

openalex publication_date 2022/10/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We present convergence analysis towards a numerical scheme designed for Q-tensor flows of nematic liquid crystals. This scheme is based on the Invariant Energy Quadratization method, which introduces an auxiliary variable to replace the original energy functional. In this work, we have shown that given an initial value with H² regularity, we can obtain a uniform H² estimate on the numerical solutions for Q-tensor flows and then deduce the convergence to a strong solution of the parabolic-type Q-tensor equation. We have also shown that the limit of the auxiliary variable is equivalent to the original energy functional term in the strong sense.

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