Description:
In this paper, we rigorously study an order 2 (in time) scheme for the numerical integration of the Landau-Lifschitz-Gilbert (LLG) equations in their full complexity, in particular including stray-field interactions. The scheme combines a linear inner iteration with a non-linear renormalization stage. A rigorous proof of convergence of the numerical solution toward a weak solution is given, when both space and time stepsize tend to 0. A numerical implementation of the scheme shows its performance on physically relevant test cases. We point out that to the knowledge of the authors this is the first finite element scheme for the LLG equations which enjoys such theoretical and practical properties.