论文标题
部分可观测时空混沌系统的无模型预测
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation
论文作者
论文摘要
我们考虑弱T练运操作员的近似值。确保其收敛性的主要属性是近似值的规律性（在离散近似方案的词汇中）。在先前的工作中，存在离散运算符$ t_n $的存在，这些$ T_N $在离散标准中收敛到$ t $，足以获得规律性。尽管事实证明，对于某些实例，这一框架对以前的假设过于强大。因此，在本文中，我们报告了一个较弱的标准，离散运算符$ t_n $仅必须在点上汇合，但此外，弱T-矫正条件必须在离散级别上得到满足。我们应用新框架来证明阻尼时谐波的加尔布伦方程的某些$ h^1 $合并有限元离散化的收敛性，该方程用于建模恒星的振荡。后者分析中的主要成分是差异操作员在某些空间上的统一稳定的反转性，这与Stokes方程的无差异元素主题有关。
We consider the approximation of weakly T-coercive operators. The main property to ensure the convergence thereof is the regularity of the approximation (in the vocabulary of discrete approximation schemes). In a previous work the existence of discrete operators $T_n$ which converge to $T$ in a discrete norm was shown to be sufficient to obtain regularity. Although this framework proved useful for many applications for some instances the former assumption is too strong. Thus in the present article we report a weaker criterion for which the discrete operators $T_n$ only have to converge point-wise, but in addition a weak T-coercivity condition has to be satisfied on the discrete level. We apply the new framework to prove the convergence of certain $H^1$-conforming finite element discretizations of the damped time-harmonic Galbrun's equation, which is used to model the oscillations of stars. A main ingredient in the latter analysis is the uniformly stable invertibility of the divergence operator on certain spaces, which is related to the topic of divergence free elements for the Stokes equation.
