  Spin currents act on ferromagnets by exerting a torque on the magnetisation.
This torque is modelled by appending additional terms to the
Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous
Landau-Lifshitz-Gilbert equation. We first prove the existence and uniqueness
of high regularity local solutions to this equation using the Faedo-Galerkin
method. Then we construct a numerical method for the problem and prove that it
converges to a global weak solution of the PDE. Numerical simulations of the
problem are also included.
