OPTIMAL ERROR ANALYSIS OF PARTIALLY-UPDATED PROJECTION FEM SCHEME FOR THE LANDAU-LIFSHITZ EQUATION BASED ON THE CRANK-NICOLSON DISCRETIZATION

Guomei Zhao; Rong An

doi:10.11948/20210193

2021 Volume 11 Issue 6

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Guomei Zhao, Rong An. OPTIMAL ERROR ANALYSIS OF PARTIALLY-UPDATED PROJECTION FEM SCHEME FOR THE LANDAU-LIFSHITZ EQUATION BASED ON THE CRANK-NICOLSON DISCRETIZATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3115-3132. doi: 10.11948/20210193

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Guomei Zhao, Rong An. OPTIMAL ERROR ANALYSIS OF PARTIALLY-UPDATED PROJECTION FEM SCHEME FOR THE LANDAU-LIFSHITZ EQUATION BASED ON THE CRANK-NICOLSON DISCRETIZATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 3115-3132. doi: 10.11948/20210193

OPTIMAL ERROR ANALYSIS OF PARTIALLY-UPDATED PROJECTION FEM SCHEME FOR THE LANDAU-LIFSHITZ EQUATION BASED ON THE CRANK-NICOLSON DISCRETIZATION

Guomei Zhao¹,
Rong An^1, ,

1.
College of Mathematics and Physics, Wenzhou University, 325035 Wenzhou, China

Corresponding author: Email: anrong@wzu.edu.cn(R. An)
Fund Project: The authors were supported by National Natural Science Foundation of China (11771337)

Abstract

Abstract

This paper presents a Crank-Nicolson partially-updated projection finite element scheme for the numerical approximation of the Landau-Lifshitz equation which describes the dynamics of magnetization in ferromagnetic materials and is a strongly nonlinear parabolic problem with the non-convex constraint. The proposed scheme is a semi-implicit scheme by using the extrapolation technique and the implicit-explicit method to linearize the nonlinear terms. Furthermore, the sphere projection is used to preserve the unit length such that numerical solutions satisfy the non-convex constraint exactly. The optimal second-order convergence rate in time and space is derived under the reasonable time step condition. Finally, the numerical experiment is presented to confirm the theoretical result.
- Landau-Lifshitz equation /
- Crank-Nicolson scheme /
- sphere projection method /
- finite element method /
- error analysis
MSC: 65N12, 65N30, 35K61

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References

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