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 \(\| P\|=\|I-P \|\) for any nontrivial idempotent operator P. Some remarks are also made on the Brezzi's theory for mixed variational problems and their Galerkin approximations.
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Received March 1, 2000 / Revised version received September 28, 2000 / Published online June 17, 2002
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ID="*" This work was partially supported by NSF DMS-9706949, NSF ACI-9800244 and NASA NAG2-1236
Correspondence to: J. Xu
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Xu, J., Zikatanov, L. Some observations on Babu\vs}ka and Brezzi theories. Numer. Math. 94, 195–202 (2003). https://doi.org/10.1007/s002110100308
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DOI: https://doi.org/10.1007/s002110100308