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({\delta}t) in the sense of L2 norm, where {\delta}t is the time step.Finally, we give some numerical simulations to demonstrate the theoretical analysis.

翻译：本文针对三维向列相液晶流体动力学Q张量模型，提出了一种一阶无条件能量稳定格式的严格误差估计。该格式将标量辅助变量法、稳定化方法和投影法相结合，证明了格式的唯一可解性和能量耗散特性。通过数学推导，进一步获得了数值解在L^{\infty}范数下的有界性。在此基础上，我们给出了时间步长{\delta}t在L2范数意义下阶数为O({\delta}t)的严格误差估计。最后，通过数值模拟验证了理论分析的正确性。