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

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).

33 pages,60 figures