## Variational principles for the momentum equation
of mantle convection with Newtonian and power-law rheologies

**Ctirad Matyska**
### Summary

Variational principles for the momentum equation with neglected inertial
forces are formulated both for Newtonian and power-law rheologies
and their theoretical functional justification is demonstrated.
The existence and uniqueness of the solution are proved and general gradient
optimization techniques prior to discretization are studied. Difficulties with
the transformation of the nonlinear problem to a series of linear problems
are outlined.
To avoid powers of the nabla operator, that appear when the principles
are expressed only in terms of velocities,
an alternative hybrid variational
principle expressed in terms of velocities and stresses is suggested.

Geophys. J. Int., **126** (1996), 281-286.