A convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation

We propose a convergent finite-element-based discretization of the stochastic Landau-Lifshitz-Gilbert equation. The main difficulties in the convergence analysis for this nonlinear stochastic partial differential equation are to properly address the pointwise sphere condition and, in the fully discrete scheme, the Stratonovich noise. Approximations of the scheme proposed here satisfy a sphere constraint at nodal points of the spatial discretization and have finite energies, and their increments may be controlled uniformly with respect to discretization parameters. Sequences of corresponding continuified processes may then be generated which construct weak martingale solutions of the limiting equations.