Numerische Mathematik

, Volume 94, Issue 1, pp 195–202

Some observations on Babu\vs}ka and Brezzi theories

  • Jinchao Xu
  • Ludmil Zikatanov
Original article

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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jinchao Xu
    • 1
  • Ludmil Zikatanov
    • 1
  1. 1.Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA; e-mail: {xu,ltz}@math.psu.edu US

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