### 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 |
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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.