An estimate of the Babuška–Brezzi inf–sup discrete stability constant for general linear Petrov–Galerkin finite element formulations (an estimate of the Babuška–Brezzi stability constant)

摘要

An a priori lower bound estimate of the Babuška–Brezzi (BB) inf–sup discrete stability constant is given for general linear Petrov–Galerkin formulations. The estimate is based on reasonable assumptions regarding a specific auxiliary adjoint problem. The similarities and discrepancies of the presented method, compared to the well known Fortin’s criterion, are also noted. The estimate may be used to obtain numerical verification of the BB condition, under the assumption that the finite element basis functions are almost orthogonal.