### 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 language | English |
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Pages (from-to) | 521-531 |

Number of pages | 11 |

Journal | Future Generation Computer Systems |

Volume | 22 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2006 Mar |

Externally published | Yes |

### Fingerprint

### 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

**Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients - Thermal convection problems in a spherical shell.** / Tabata, Masahisa.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients - Thermal convection problems in a spherical shell

AU - Tabata, Masahisa

PY - 2006/3

Y1 - 2006/3

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

UR - http://www.scopus.com/inward/record.url?scp=29644439196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29644439196&partnerID=8YFLogxK

U2 - 10.1016/j.future.2005.04.008

DO - 10.1016/j.future.2005.04.008

M3 - Article

AN - SCOPUS:29644439196

VL - 22

SP - 521

EP - 531

JO - Future Generation Computer Systems

JF - Future Generation Computer Systems

SN - 0167-739X

IS - 4

ER -