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

An a priori lower bound estimate of the Babuska-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. (C) 2002 Elsevier Science Inc. All rights reserved.