Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients - Thermal convection problems in a spherical shell

Masahisa Tabata

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with temperature-dependent coefficients is analyzed. The domain is a spherical shell and the P1-element is employed for every unknown function. The finite element solution is proved to converge to the exact one in the first order of the time increment and the mesh size. The scheme is applied to Earth's mantle convection problems with viscosities strongly dependent on the temperature and some numerical results are shown.

Original languageEnglish
Pages (from-to)521-531
Number of pages11
JournalFuture Generation Computer Systems
Volume22
Issue number4
DOIs
Publication statusPublished - 2006 Mar
Externally publishedYes

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Prandtl number
Earth (planet)
Viscosity
Temperature
Convection
Hot Temperature

Keywords

  • Infinite Prandtl number Boussinesq equations
  • Stabilized finite element scheme
  • Temperature-dependent coefficients
  • Thermal convection problems

ASJC Scopus subject areas

  • Computer Science Applications
  • Hardware and Architecture
  • Control and Systems Engineering

Cite this

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abstract = "A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with temperature-dependent coefficients is analyzed. The domain is a spherical shell and the P1-element is employed for every unknown function. The finite element solution is proved to converge to the exact one in the first order of the time increment and the mesh size. The scheme is applied to Earth's mantle convection problems with viscosities strongly dependent on the temperature and some numerical results are shown.",
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N2 - A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with temperature-dependent coefficients is analyzed. The domain is a spherical shell and the P1-element is employed for every unknown function. The finite element solution is proved to converge to the exact one in the first order of the time increment and the mesh size. The scheme is applied to Earth's mantle convection problems with viscosities strongly dependent on the temperature and some numerical results are shown.

AB - A stabilized finite element scheme for infinite Prandtl number Boussinesq equations with temperature-dependent coefficients is analyzed. The domain is a spherical shell and the P1-element is employed for every unknown function. The finite element solution is proved to converge to the exact one in the first order of the time increment and the mesh size. The scheme is applied to Earth's mantle convection problems with viscosities strongly dependent on the temperature and some numerical results are shown.

KW - Infinite Prandtl number Boussinesq equations

KW - Stabilized finite element scheme

KW - Temperature-dependent coefficients

KW - Thermal convection problems

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