Fourier analysis of stabilized Q1-Q1 mixed finite element approximation

Sean Norburn; David Silvester

doi:10.1137/S0036142999362274

Fourier analysis of stabilized Q1-Q1 mixed finite element approximation

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

Abstract

We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible flow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya-Babuška-Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter.

Original language	English
Pages (from-to)	817-833
Number of pages	16
Journal	SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume	39
Issue number	3
DOIs	https://doi.org/10.1137/S0036142999362274
Publication status	Published - 2002

Keywords

Finite element
Mixed approximation
Stabilization

Access to Document

10.1137/S0036142999362274

Cite this

@article{b1e27dd548554daab2143d6b62bcc824,

title = "Fourier analysis of stabilized Q1-Q1 mixed finite element approximation",

abstract = "We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible flow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya-Babu{\v s}ka-Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter.",

keywords = "Finite element, Mixed approximation, Stabilization",

author = "Sean Norburn and David Silvester",

year = "2002",

doi = "10.1137/S0036142999362274",

language = "English",

volume = "39",

pages = "817--833",

journal = "SIAM JOURNAL ON NUMERICAL ANALYSIS",

publisher = "Society for Industrial and Applied Mathematics",

number = "3",

}

TY - JOUR

T1 - Fourier analysis of stabilized Q1-Q1 mixed finite element approximation

AU - Norburn, Sean

AU - Silvester, David

PY - 2002

Y1 - 2002

N2 - We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible flow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya-Babuška-Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter.

AB - We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible flow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya-Babuška-Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter.

KW - Finite element

KW - Mixed approximation

KW - Stabilization

U2 - 10.1137/S0036142999362274

DO - 10.1137/S0036142999362274

M3 - Article

VL - 39

SP - 817

EP - 833

JO - SIAM JOURNAL ON NUMERICAL ANALYSIS

JF - SIAM JOURNAL ON NUMERICAL ANALYSIS

IS - 3

ER -

Fourier analysis of stabilized Q1-Q1 mixed finite element approximation

Abstract

Keywords

Access to Document

Fingerprint

Cite this