Spectral variational approach to the non-Newtonian stokes problem in a spherical shell

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Abstract

A hybrid-variational formulation of the Stokes equation for incompressible non-Newtonian flow is suggested. A spherical harmonic technique is adopted to discretize the problem. In the case of non-Newtonian rheology, the energy functional becomes non-quadratic. To minimize it on the set of admissible stress-functions, the gradient method is used and the convergence of the method is demonstrated.

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