Maximum bound principle for Q-tensor gradient flow with low regularity integrators

2025/04/16 by Wenshuai Hu, Hu, Wenshuai, Guanghua Ji +1 · 1 citation
Engineering · Medicine · Physics and Astronomy · #65M06 #Advanced Neuroimaging Techniques and Applications #Convergence (economics) #Cosmology and Gravitation Theories #Dissipation #Eigenvalues and eigenvectors #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #G.1.8 #Integrator #Numerical Analysis (math.NA) #Range (aeronautics) #Upper and lower bounds #Work (physics)

paper · pdf · doi:10.48550/arxiv.2504.11676

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate low-regularity integrator (LRI) methods for the Q-tensor model governing nematic liquid-crystalline semilinear parabolic equation. First- and second-order temporal discretizations are developed using Duhamel's formula, and we rigorously prove that both schemes preserve the maximum bound principle (MBP) and energy dissipation under minimal regularity requirements. Optimal convergence rates are established for the proposed methods. Numerical experiments validate the theoretical findings, demonstrating that the eigenvalues of Q remain strictly confined within the physical range (-1/3,2/3).

Citations

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Cited by

• On the maximum bound principle and energy dissipation of exponential time differencing methods for the chiral liquid crystal blue phases

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