2024
DOI: 10.1093/imanum/drae046
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Numerical method and error estimate for stochastic Landau–Lifshitz–Bloch equation

Beniamin Goldys,
Chunxi Jiao,
Kim-Ngan Le

Abstract: In this paper we study numerical methods for solving a system of quasilinear stochastic partial differential equations known as the stochastic Landau–Lifshitz–Bloch (LLB) equation on a bounded domain in ${\mathbb{R}}^{d}$ for $d=1,2$. Our main results are estimates of the rate of convergence of the Finite Element Method to the solutions of stochastic LLB. To overcome the lack of regularity of the solution in the case $d=2$, we propose a Finite Element scheme for a regularized version of the equation. We then o… Show more

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