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A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction. (English) Zbl 1334.78040

The paper concerns the coupled system of the Landau-Lifshitz-Gilbert equation and the conservation of momentum equation that allows to take into account magnetostrictive effects. The authors propose a numerical scheme based on linear finite elements in space and a linear-implicit Euler discretization in time. Even if the problem is highly non-linear the scheme requires to solve only two linear systems in each time step. The authors prove the convergence of at least a subsequence towards a weak solution of the continuous coupled problem. In this way the authors provide an alternative proof of the existence of weak solutions. The paper includes some numerical experiments that illustrate the performance of the scheme and study the discrete blow-up of the Landau-Lifshitz-Gilbert equation, in particular the influence of the magnetostrictive term.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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