• Corpus ID: 244117076

Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters

  title={Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters},
  author={Yongyong Cai and Jingrun Chen and Cheng Wang and Changjian Xie},
A second order accurate, linear numerical method is analyzed for the LandauLifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non-convexity constraint of unit length of the magnetization. The numerical method is based on the second-order backward differentiation formula in time, combined with an implicit treatment of the linear diffusion term and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to… 



Analysis of a fourth order finite difference method for the incompressible Boussinesq equations

Summary.The convergence of a fourth order finite difference method for the 2-D unsteady, viscous incompressible Boussinesq equations, based on the vorticity-stream function formulation, is

Optimal Error Estimates of a Linearized Backward Euler FEM for the Landau-Lifshitz Equation

  • Huadong Gao
  • Computer Science, Mathematics
    SIAM J. Numer. Anal.
  • 2014
We present a fully discrete linearized backward Euler finite element method for the Landau--Lifshitz equation in which a new linearization is proposed for the gyromagnetic term. Optimal almost

Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation

Stability and optimal-order error bounds in the situation of a sufficiently regular solution are proved and a discrete energy bound irrespective of solution regularity is obtained.

Convergence analysis for second‐order accurate schemes for the periodic nonlocal Allen‐Cahn and Cahn‐Hilliard equations

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A theoretical analysis of the proposed gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field a and a gauge variable Φ, u = a + ⊇Φ and it is proved first order convergence of the gauge method when the authors use MAC grids as their spatial discretization.

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Optimal Error Estimates of Linearized Crank–Nicolson Galerkin Method for Landau–Lifshitz Equation

  • R. An
  • Mathematics
    J. Sci. Comput.
  • 2016
The proof of the optimal error estimates are based upon an error splitting technique proposed by Li and Sun and are provided to confirm the regularity of the local strong solution to LL equation with Neumann boundary conditions.