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

Authors:
Masahisa Tabata
Affiliations:
Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, Japan
Venue:
Future Generation Computer Systems
Year:
2006

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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 PI-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.