Numerische Mathematik

, Volume 94, Issue 1, pp 195–202

Some observations on Babu\vs}ka and Brezzi theories

Authors

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

DOI: 10.1007/s002110100308

Cite this article as:
Xu, J. & Zikatanov, L. Numer. Math. (2003) 94: 195. doi:10.1007/s002110100308

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

Copyright information

© Springer-Verlag Berlin Heidelberg 2002