A POSTERIORI ERROR ANALYSIS OF THE INF-SUP CONSTANT FOR THE DIVERGENCE

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.

Automated summary

Two a posteriori error estimates for the inf-sup constant are presented, providing upper and lower bounds for eigenvalue and eigenfunction errors, with a convergence of the reliability constant to 1 as mesh size decreases for guaranteed enclosures of the inf-sup constant on sufficiently fine meshes. Suboptimal efficiency estimate is noted for the second error estimate.