In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed with the help of appropriate $L^2$ error estimates. A priori and a posteriori estimates are proved.

中文翻译：

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特征值问题的一阶最小二乘公式

在本文中，我们讨论了与椭圆偏微分方程的最小二乘有限元近似相关的算子的谱特性。借助适当的 $L^2$ 误差估计，研究和分析了离散特征值和特征函数向相应连续特征模态的收敛性。证明了先验和后验估计。