L. Banas, M. Page, D. Praetorius, J. Rochat:
"On the Landau-Lifshitz-Gilbert equations with magnetostriction";
IMA J. Numer. Anal., 34 (2014), 4; S. 1361 - 1385.

Kurzfassung englisch:
To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system
of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum
equation. This coupling allows to include magnetostrictive effects into the simulations.
Existence of weak solutions has recently been shown in [CARBOU ET AL., Math. Meth. Appl.
Sci. (2011)]. In our contribution, we give an alternate proof which additionally provides an
effective numerical integrator. The latter is based on linear finite elements in space and a
linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear systems have to
be solved per timestep, and the integrator fully decouples both equations. Finally, we prove
unconditional convergence-at least of a subsequence-towards, and hence existence of, a
weak solution of the coupled system, as timestep size and spatial mesh-size tend to zero. We
conclude the work with numerical experiments which study the discrete blow-up of the LLG
equation as well as the influence of the magnetostrictive term on the discrete blow-up.

LLG, magnetostriction, linear scheme, ferromagnetism, convergence.

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