On the convergence of an unconditionally stable numerical scheme for the Q-tensor flow based on the invariant quadratization method

Abstract

We present a 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 show that given an initial value with H2 regularity, we can obtain a uniform H2 estimate on the numerical approximations for the Q-tensor flows and then deduce the convergence to a strong solution of the parabolic-type Q-tensor equation. We also show that the limit of the auxiliary variable is equivalent to the original energy functional term in the strong sense.