Error estimate for the first order energy stable scheme of Q-tensor nematic model

We present rigorous error estimates towards a first-order unconditionally energy stable scheme designed for 3D hydrodynamic Q-tensor model of nematic liquid crystals. This scheme combines the scalar auxiliary variable (SAV), stabilization and projection method together. The unique solvability and energy dissipation of the scheme are proved. We further derive the boundness of numerical solution in L^{\infty} norm with mathematical deduction. Then, we can give the rigorous error estimate of order O(δt) in the sense of L2 norm, where δt is the time step.Finally, we give some numerical simulations to demonstrate the theoretical analysis.