用于二阶椭圆偏微分方程的首阶系统LL*（FOSLL*）方法
Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations
AI总结：
本文提出用于二阶椭圆偏微分方程的首阶系统LL*方法，建立了其well-posedness，并在不依赖小网格尺寸的情况下获得了近优的先验误差界。
摘要：
在[10]中，针对一般二阶椭圆偏微分方程提出了首阶系统LL*（FOSLL*）方法，旨在保留L2范数首阶系统最小二乘（FOSLS）方法的全部效率，同时具有逆范数FOSLS方法的通用性。[10]中的FOSLL*方法应用于div-curl系统并添加了松弛变量，因此相当复杂。本文将FOSLL*方法应用于div系统并建立了其well-posedness。对于相应的有限元近似，我们在与标准Galerkin方法相同的正则性假设下获得了近优的先验误差界，但不依赖于足够小的网格尺寸。与FOSLS方法不同，FOSLL*方法没有自由的后验误差估计器，我们则提出了显式的残差误差估计器，并建立了其可靠性和效率界。
英文摘要：
The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS) ap- proach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the div-curl system with added slack vari- ables, and hence it is quite complicated. In this paper, we apply the FOSLL* approach to the div system and establish its well-posedness. For the corresponding finite ele- ment approximation, we obtain a quasi-optimal a priori error bound under the same regularity assumption as the standard Galerkin method, but without the restriction to sufficiently small mesh size. Unlike the FOSLS approach, the FOSLL* approach does not have a free a posteriori error estimator, we then propose an explicit residual error estimator and establish its reliability and efficiency bounds
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