Q张量向列相模型一阶能量稳定格式的误差估计
Error estimate for the first order energy stable scheme of Q-tensor nematic model
AI总结：
针对三维向列相液晶流体动力学Q张量模型，研究结合SAV、稳定化与投影法的一阶无条件能量稳定格式，证明其唯一可解性、能量耗散性与L∞范数有界性，推导L2范数下O(δt)的误差估计，并通过数值模拟验证理论结果。
摘要：
我们针对向列相液晶的三维流体动力学Q张量模型所设计的一阶无条件能量稳定格式，给出了严格的误差估计。该格式结合了标量辅助变量（SAV，scalar auxiliary variable）方法、稳定化方法与投影法。我们证明了该格式的唯一可解性与能量耗散性，进一步通过数学推导得出数值解在L^{\u221e}范数下的有界性。随后我们给出了L2范数意义下阶数为O(δt)的严格误差估计，其中δt为时间步长。最后我们通过若干数值模拟验证了该理论分析。
英文摘要：
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.
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