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

Ctirad Matyska


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.