  A Galerkin finite element (FEM) formulation for the Bloch equations with
dipolar field is presented which makes possible the derivation of weak
solutions to the Bloch equations. The FEM formulation has the advantage that
the equations of motion are local in real space, eliminating the global
truncation errors associated with calculations of the dipolar field in Fourier
space. The dipolar field and other geometric parameters are calculated only
once, before the simulation, and used as an initial condition rather than
re-calculated at every time step of some numerical integration.
