Some observations on Babu\vs}ka and Brezzi theories

Summary. Some observations are made on abstract error estimates for Galerkin approximations based on Babuška-Brezzi conditions. A basic error estimate due to Babuška is sharpened by means of an identity that for any nontrivial idempotent operator P. Some remarks are also made on the Brezzi's theory for mixed variational problems and their Galerkin approximations. Received March 1, 2000 / Revised version received September 28, 2000 / Published online June 17, 2002 RID="*" ID="*" This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236 Correspondence to: J. Xu