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

137 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 1 2003
Externally published	Yes

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s002110100308

Cite this

@article{bf078e400c214ffdb0466ed1d527189c,

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",

note = "Generated from Scopus record by KAUST IRTS on 2023-02-15",

year = "2003",

month = mar,

day = "1",

doi = "10.1007/s002110100308",

language = "English (US)",

volume = "94",

pages = "195--202",

journal = "Numerische Mathematik",

issn = "0029-599X",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Some observations on Babuška and Brezzi theories

AU - Xu, Jinchao

AU - Zikatanov, Ludmil

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2003/3/1

Y1 - 2003/3/1

N2 - 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.

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.

UR - http://link.springer.com/10.1007/s002110100308

UR - http://www.scopus.com/inward/record.url?scp=0142023257&partnerID=8YFLogxK

U2 - 10.1007/s002110100308

DO - 10.1007/s002110100308

M3 - Article

SN - 0029-599X

VL - 94

SP - 195

EP - 202

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 1

ER -

Some observations on Babuška and Brezzi theories

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this