COMPUTATION OF THE LBB CONSTANT FOR THE STOKES EQUATION WITH A LEAST-SQUARES FINITE ELEMENT METHOD

An investigation of a least-squares finite element method (LSFEM) for the Stokes equation reveals a relation of the Ladyzhenslaya-Babugka-Brezzi (LBB) constant and the ellipticity constants of the LSFEM. While the approximation of the LBB constant with standard numerical methods is challenging, the approximation of the ellipticity constants is in a Rayleigh-Ritz-like environment. This setting is well understood and so allows for an easy-to-implement convergent numerical scheme for the computation of the LBB constant. Numerical experiments with uniform and adaptive mash refinements complement the investigation of this novel scheme.