Some observations on Babuška and Brezzi theories

Jinchao Xu; Ludmil Zikatanov

doi:10.1007/s002110100308

Some observations on Babuška and Brezzi theories

Jinchao Xu
, Ludmil Zikatanov

Research output: Contribution to journal › Article › peer-review

149 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	195-202
Number of pages	8
Journal	Numerische Mathematik
Volume	94
Issue number	1
DOIs	https://doi.org/10.1007/s002110100308
State	Published - Mar 2003

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1007/s002110100308

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title = "Some observations on Babu{\v s}ka and Brezzi theories",

abstract = "Some observations are made on abstract error estimates for Galerkin approximations based on Babu{\v s}ka-Brezzi conditions. A basic error estimate due to Babu{\v s}ka 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.",

author = "Jinchao Xu and Ludmil Zikatanov",

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AB - 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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Some observations on Babuška and Brezzi theories

Abstract

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