SIAM Journal on Numerical Analysis, Volume 59, Issue 1, Page 249-264, January 2021.
Two a posteriori error estimates for a numerical approximation scheme for the inf-sup constant for the divergence (also known as the LBB constant) are shown. Under the assumption that the inf-sup constant is an eigenvalue of the Cosserat operator separated from the essential spectrum and that the mesh size is sufficiently small, the first estimate bounds the eigenvalue and eigenfunction errors from above and below by an error estimator up to multiplicative constants. In the second error estimate the reliability constant converges to 1 as the mesh size decreases, at the expense of a suboptimal efficiency estimate, and so allows for guaranteed enclosures of the inf-sup constant on sufficiently fine meshes.

中文翻译：

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发散常数的后验误差分析

SIAM数值分析杂志，第59卷，第1期，第249-264页，2021年1月。显示了
两个用于发散的inf-sup常数（也称为LBB常数）的数值近似方案的后验误差估计。假设inf-sup常数是Cosserat算子的特征值与基本谱分开，并且网格大小足够小，则第一估计将误差估计器从上至下限制本征值和本征函数误差，直至乘积常数。在第二个误差估计中，随着网格尺寸的减小，可靠性常数收敛到1，这是以次优效率估计为代价的，因此可以保证将inf-up常数封装在足够精细的网格上。