A convergent and precise finite element scheme for Landau-Lifschitz-Gilbert equation (Q471192)

The authors propose a new finite element scheme for the Landau-Lifschitz-Gilbert equation and they prove that it is consistent up to order two in time. The new method is a generalization of the scheme proposed by \textit{F. Alouges} [Discrete Contin. Dyn. Syst., Ser. S 1, No. 2, 187--196 (2008; Zbl 1152.35304)]. Even if the problem is highly non-linear the scheme requires only the solution of a linear and positive definite system in each time step. The authors prove convergence of the numerical solution toward a weak solution of the continuous problem. Two numerical experiments on physically relevant test cases illustrate the performance of the scheme and confirm the order in time.