Finite element approximation to infinite Prandtl number Boussinesq equations with temperature dependent viscosity and its application to Earth s mantle convection problem

A stabilized finite element scheme for infinite Prandtl number Boussinesq
equations with temperature dependent viscosity 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.