VARIATIONAL-PRINCIPLES FOR THE MOMENTUM EQUATION OF MANTLE CONVECTIONWITH NEWTONIAN AND POWER-LAW RHEOLOGIES

Variational principles for the momentum equation with neglected inerti al forces are formulated for both Newtonian and power-law rheologies, and their theoretical functional justification is demonstrated. The ex istence and uniqueness of the solution are proved, and general gradien t optimization techniques prior to discretization are studied. Difficu lties with the transformation of the non-linear problem to a series of linear problems are outlined. To avoid powers of the nabla operator, which appear when the principles are expressed only in terms of veloci ties, an alternative hybrid variational principle expressed in terms o f velocities and stresses is suggested.