Weak martingale solutions to the stochastic Landau–Lifshitz–Gilbert equation with multi-dimensional noise via a convergent finite-element scheme

Beniamin Goldys, Joseph F. Grotowski and Kim-Ngan Le

Stochastic Processes and their Applications, 2020, vol. 130, issue 1, 232-261

Abstract: We propose an unconditionally convergent linear finite element scheme for the stochastic Landau–Lifshitz–Gilbert (LLG) equation with multi-dimensional noise. By using the Doss–Sussmann technique, we first transform the stochastic LLG equation into a partial differential equation that depends on the solution of the auxiliary equation for the diffusion part. The resulting equation has solutions absolutely continuous with respect to time. We then propose a convergent θ-linear scheme for the numerical solution of the reformulated equation. As a consequence, we are able to show the existence of weak martingale solutions to the stochastic LLG equation.

Keywords: Stochastic partial differential equation; Landau–Lifshitz–Gilbert equation; Finite element; Ferromagnetism (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:1:p:232-261

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DOI: 10.1016/j.spa.2019.02.011

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