### Abstract

A finite element scheme is developed and analyzed for a thermal convection problem of Boussinesq fluid with infinite Prandtl number in a spherical shell. This problem is a mathematical model of the Earth's mantle movement and has been a topic of interest for geophysicists. It is described by the Rayleigh-Benard equations with infinite Prandtl number, that is, a system of the Stokes equations and the convection-diffusion equation coupled with the buoyancy and the convection terms. A stabilized finite element scheme with P1/P1/P1 element is presented, and an error estimate is established. The obtained theoretical convergence order is also recognized by a numerical result. Another numerical result is shown as an example of the Earth's mantle movement simulation.

Original language | English |
---|---|

Pages (from-to) | 387-402 |

Number of pages | 16 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 190 |

Issue number | 3-4 |

Publication status | Published - 2000 Oct 27 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computer Science Applications
- Computational Mechanics

### Cite this

*Computer Methods in Applied Mechanics and Engineering*,

*190*(3-4), 387-402.

**Stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell.** / Tabata, M.; Suzuki, A.

Research output: Contribution to journal › Article

*Computer Methods in Applied Mechanics and Engineering*, vol. 190, no. 3-4, pp. 387-402.

}

TY - JOUR

T1 - Stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell

AU - Tabata, M.

AU - Suzuki, A.

PY - 2000/10/27

Y1 - 2000/10/27

N2 - A finite element scheme is developed and analyzed for a thermal convection problem of Boussinesq fluid with infinite Prandtl number in a spherical shell. This problem is a mathematical model of the Earth's mantle movement and has been a topic of interest for geophysicists. It is described by the Rayleigh-Benard equations with infinite Prandtl number, that is, a system of the Stokes equations and the convection-diffusion equation coupled with the buoyancy and the convection terms. A stabilized finite element scheme with P1/P1/P1 element is presented, and an error estimate is established. The obtained theoretical convergence order is also recognized by a numerical result. Another numerical result is shown as an example of the Earth's mantle movement simulation.

AB - A finite element scheme is developed and analyzed for a thermal convection problem of Boussinesq fluid with infinite Prandtl number in a spherical shell. This problem is a mathematical model of the Earth's mantle movement and has been a topic of interest for geophysicists. It is described by the Rayleigh-Benard equations with infinite Prandtl number, that is, a system of the Stokes equations and the convection-diffusion equation coupled with the buoyancy and the convection terms. A stabilized finite element scheme with P1/P1/P1 element is presented, and an error estimate is established. The obtained theoretical convergence order is also recognized by a numerical result. Another numerical result is shown as an example of the Earth's mantle movement simulation.

UR - http://www.scopus.com/inward/record.url?scp=0034287407&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034287407&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034287407

VL - 190

SP - 387

EP - 402

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 3-4

ER -