## The Stokes problem with 3-D Newtonian rheology in a sphericall shell

**Zdenek Martinec** ** , **
**Ctirad Matyska** ** , **
**Ondrej Cadek** ** & **
**P. Hrdina**
### Summary

A variational approach is used to solve the
linear Stokes problem with a three-dimensional viscosity in a spherical
shell. A semi-spectral
method is proposed to discretize the problem. To minimize the energy
functional on the set of admissible velocities, the gradient method with
a corresponding projection is employed. The numerical behavior
is satisfactory and the method can be employed in studies
of planetary interiors with complex rheological structures.

Computer Physics Communication, **76** (1993), 63-79.