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The motion of glaciers can be simulated with the p-Stokes equations. Wepresent an algorithm that solves these equations faster than the Picarditeration. We do that by proving q-superlinear global convergence of theinfinite-dimensional Newton's method with Armijo step sizes to the solution ofthese equations. We only have to add an arbitrarily small diffusion term forthis convergence result. We also consider approximations of exact step sizes.Exact step sizes are possible because we reformulate the problem as minimizinga convex functional. Next, we prove that the additional diffusion term onlycauses minor differences in the solution compared to the original p-Stokesequations. Finally, we test our algorithms on a reformulation of the experimentISMIP-HOM B. The approximation of exact step sizes for the Picard iteration andNewton's method is superior in the experiment compared to the Picard iteration.Also, Newton's method with Armijo step sizes converges faster than the Picarditeration. However, the reached accuracy of Newton's method with Armijo stepsizes depends more on the resolution of the domain.

Global q-superlinear convergence of the infinite-dimensional Newton's method for the regularized p-Stokes equations