Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation
نویسندگان
چکیده
منابع مشابه
Convergence of an Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation
The Landau-Lifshitz-Gilbert equation describes dynamics of ferromagnetism, where strong nonlinearity, nonconvexity are hard to tackle: so far, existing schemes to approximate weak solutions suffer from severe time-step restrictions. In this paper, we propose an implicit fully discrete scheme and verify unconditional convergence.
متن کاملSMA An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction
The Landau-Lifshitz-Gilbert Equation describes the dynamics of ferromagnetism, where strong nonlinearity and non-convexity are hard to tackle. Based on the work of S.Bartels and A.Prohl "Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation" ([4]), we present in this report a fully implicit finite element scheme with exchange and magnetostriction. We verify u...
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We propose a finite difference scheme for the Heisenberg equation and the LandauLifshitz equation. These equations have a length-preserving property and energy conservation or dissipation property. Our proposed scheme inherits both characteristic properties. We also show that the boundedness of finite difference solutions and an unique solvability of our scheme. Finally, we show some numerical ...
متن کاملFinite Time Singularity of the Landau-Lifshitz-Gilbert Equation
We prove that in dimensions three or four, for suitably chosen initial data, the short time smooth solution to the Landau-Lifshitz-Gilbert equation blows up at finite time.
متن کاملIsotropic Landau-Lifshitz Equation
By using the geometric concept of PDEs with prescribed curvature representation, we prove that the 1+2 dimensional isotropic Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schrödinger-type system. From the nonlinear Schrödinger-type system, we construct blowing up H3(R2)-solutions to the Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2017
ISSN: 0033-569X,1552-4485
DOI: 10.1090/qam/1485