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The Landau-Lifshitz-Bloch Equation With Spin Diffusion: Global Strong Solution and Finite Element Approximation
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DOI：10.1002/num.70070.png)
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Abstract
En 中文
The spin-diffusion Landau-Lifshitz-Bloch (SDLLB) system is a nonlinearly coupled system of quasilinear vector-valued PDEs which models the interaction between spin-polarised currents and magnetisation at high temperatures. The aim of this paper is twofold. Firstly, assuming the initial data is sufficiently small, we show the existence of a unique global strong solution to the SDLLB equation in a bounded domain Omega subset of R-d, where d <= 3, thus ensuring well-posedness of the model. Secondly, we propose a decoupled linearised fully-discrete finite element scheme to solve the problem. Despite the strong nonlinearity of the system, the proposed scheme only requires the solution of two completely decoupled linear systems per time-step. Assuming adequate regularity of the exact solution and a certain time-step constraint, we rigorously show that the numerical scheme converges at an optimal rate. Several numerical experiments corroborate our theoretical results.
Keywords:
POLARIZED TRANSPORT
WEAK
Journal
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IF:
1.7
Papers:
46
Citations:
3.9K