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arXiv · 1212.3369

A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations

Kim-Ngan Le·T. Tran
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Abstract

We propose a $\theta$-linear scheme for the numerical solution of the quasi-static Maxwell-Landau-Lifshitz-Gilbert (MLLG) equations. Despite the strong nonlinearity of the Landau-Lifshitz-Gilbert equation, the proposed method results in a linear system at each time step. We prove that as the time and space steps tend to zero (with no further conditions when $\theta\in(1/2,1]$), the finite element solutions converge weakly to a weak solution of the MLLG equations. Numerical results are presented to show the applicability of the method.

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Kim-Ngan Le, T. Tran. 2012-12-13. A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations. https://arxiv.org/abs/1212.3369

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