论文标题
关于基于不变式构造方法的无条件稳定数值方案的收敛
On convergence of an unconditional stable numerical scheme for Q-tensor flow based on invariant quardratization method
论文作者
论文摘要
我们将收敛分析介绍针对用于列液晶Q量流的数值方案。该方案基于不变的二次化方法，该方法引入了辅助变量以替代原始能量功能。在这项工作中，我们已经证明，鉴于具有$ H^2 $规律性的初始值，我们可以在Q-Tensor流的数值解决方案上获得均匀的$ H^2 $估算值，然后将收敛推导到抛物线Q-type type type型方程的强溶液中。我们还表明，辅助变量的极限在强义中等效于原始能量功能项。
We present 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 have shown that given an initial value with $H^2$ regularity, we can obtain a uniform $H^2$ estimate on the numerical solutions for Q-tensor flows and then deduce the convergence to a strong solution of the parabolic-type Q-tensor equation. We have also shown that the limit of the auxiliary variable is equivalent to the original energy functional term in the strong sense.
