Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients

Masahisa Tabata, Daisuke Tagami

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

General error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients. These variable coefficients turn the diffusion and the buoyancy terms to be nonlinear, which increases the nonlinearity of the problems. An argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions. Error estimates are also provided for schemes modified by approximate coefficients, which are used conveniently in practical computations.

Original languageEnglish
Pages (from-to)351-372
Number of pages22
JournalNumerische Mathematik
Volume100
Issue number2
DOIs
Publication statusPublished - 2005 Apr
Externally publishedYes

Fingerprint

Thermal Convection
Error Estimates
Finite Element Method
Finite element method
Optimal Error Estimates
Dependent
Buoyancy
Energy Method
Coefficient
Variable Coefficients
Stability Condition
Nonlinearity
Finite Element
Temperature
Term
Convection
Hot Temperature
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients. / Tabata, Masahisa; Tagami, Daisuke.

In: Numerische Mathematik, Vol. 100, No. 2, 04.2005, p. 351-372.

Research output: Contribution to journalArticle

@article{3048f2adc6b0478aba74d89dc889a297,
title = "Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients",
abstract = "General error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients. These variable coefficients turn the diffusion and the buoyancy terms to be nonlinear, which increases the nonlinearity of the problems. An argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions. Error estimates are also provided for schemes modified by approximate coefficients, which are used conveniently in practical computations.",
author = "Masahisa Tabata and Daisuke Tagami",
year = "2005",
month = "4",
doi = "10.1007/s00211-005-0589-2",
language = "English",
volume = "100",
pages = "351--372",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Error estimates of finite element methods for nonstationary thermal convection problems with temperature-dependent coefficients

AU - Tabata, Masahisa

AU - Tagami, Daisuke

PY - 2005/4

Y1 - 2005/4

N2 - General error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients. These variable coefficients turn the diffusion and the buoyancy terms to be nonlinear, which increases the nonlinearity of the problems. An argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions. Error estimates are also provided for schemes modified by approximate coefficients, which are used conveniently in practical computations.

AB - General error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients. These variable coefficients turn the diffusion and the buoyancy terms to be nonlinear, which increases the nonlinearity of the problems. An argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions. Error estimates are also provided for schemes modified by approximate coefficients, which are used conveniently in practical computations.

UR - http://www.scopus.com/inward/record.url?scp=17444430435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17444430435&partnerID=8YFLogxK

U2 - 10.1007/s00211-005-0589-2

DO - 10.1007/s00211-005-0589-2

M3 - Article

VL - 100

SP - 351

EP - 372

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 2

ER -