| Citation: |
Chen Bolin, Rong An. UNCONDITIONALLY OPTIMAL CONVERGENCE ANALYSIS OF SECOND-ORDER BDF SCHEME FOR LANDAU-LIFSHITZ EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1391-1404. doi: 10.11948/20200189
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UNCONDITIONALLY OPTIMAL CONVERGENCE ANALYSIS OF SECOND-ORDER BDF SCHEME FOR LANDAU-LIFSHITZ EQUATION
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Abstract
The Landau-Lifshitz equation is used to describe the evolution of spin fields in continuum ferromagnets and is a highly nonlinear parabolic problem with the constraint of unit length in the point-wise sense. This paper focuses on the unconditionally optimal error estimates of a linearized second-order BDF scheme for the numerical approximations of the solution to the Landau-Lifshitz equation. Since the point-wise constraint can be deduced from the partial differential equation, we do not take into account it in designing the numerical scheme. A rigorous error analysis is done and we derive the unconditionally optimal $ {\textbf{L}}^2 $ error estimate by using the error splitting technique. Numerical result is shown to check the theoretical analysis.
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References
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Chen Bolin, Rong An. UNCONDITIONALLY OPTIMAL CONVERGENCE ANALYSIS OF SECOND-ORDER BDF SCHEME FOR LANDAU-LIFSHITZ EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1391-1404. doi: 10.11948/20200189
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