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

Masahisa Tabata, Daisuke Tagami

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17 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

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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