June 2023 A LINEARIZED CRANK–NICOLSON/LEAPFROG SCHEME FOR THE LANDAU–LIFSHITZ EQUATION
Mingru Liu, Pengzhan Huang, Yinnian He
Rocky Mountain J. Math. 53(3): 821-837 (June 2023). DOI: 10.1216/rmj.2023.53.821

Abstract

Based on the finite element method, a fully discrete Crank–Nicolson/leapfrog scheme is proposed and studied for the Landau–Lifshitz equation. The scheme avoids stiff time step restrictions and requires that the time step only be bounded by a constant independent of the mesh size. Then, almost unconditional optimal error estimates for the discrete scheme are obtained by using a temporal-spatial error splitting technique. The theoretical results are verified by numerical experiments.

Citation

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Mingru Liu. Pengzhan Huang. Yinnian He. "A LINEARIZED CRANK–NICOLSON/LEAPFROG SCHEME FOR THE LANDAU–LIFSHITZ EQUATION." Rocky Mountain J. Math. 53 (3) 821 - 837, June 2023. https://doi.org/10.1216/rmj.2023.53.821

Information

Received: 13 June 2022; Revised: 14 July 2022; Accepted: 18 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617914
zbMATH: 07731148
Digital Object Identifier: 10.1216/rmj.2023.53.821

Subjects:
Primary: 65M12 , 65M60

Keywords: Crank–Nicolson/leapfrog scheme , finite element method , Landau–Lifshitz equation , optimal error estimate

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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