Convergence Analysis of Numerical Schemes for Liquid Crystals Based on the Invariant Energy Quadratization Method

This thesis investigates numerical methods for various Q-tensor models of nematic liquid crystals. Originating from the Landau-de Gennes theory, the numerical discretization of the Q-tensor model presents challenges due to its high non-linearity. The thesis investigates three distinct models, each capturing the behavior of liquid crystals under different conditions: the Q-tensor model, the Q-tensor model with inertia, and the Beris-Edwards model, which connects the Q-tensor model to the Navier-Stokes equation. The numerical methods utilized are based on the Invariant Energy Quadratization (IEQ) method, a recently developed technique extensively employed in constructing energy-stable numerical schemes for gradient-flow type problems. Our studies establish several properties of the proposed methods, such as stability, convergence, and convergence rates.