Original article

Numerische Mathematik

, Volume 94, Issue 1, pp 195-202

First online:

Some observations on Babu\vs}ka and Brezzi theories

  • Jinchao XuAffiliated withDepartment of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA; e-mail: {xu,ltz}@math.psu.edu
  • , Ludmil ZikatanovAffiliated withDepartment of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA; e-mail: {xu,ltz}@math.psu.edu

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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.

Mathematics Subject Classification (1991): 65N30