Optimal error estimate of a linearized FEM based on the Lagrange multiplier approach for the Landau–Lifshitz equation

Xingwei Yang, Pengzhan Huang and Yinnian He

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 220-235

Abstract: We present a fully discrete, linearized first-order lumped mass finite element method using the Lagrange multiplier approach for the Landau–Lifshitz equation. In the presence of large damping parameter, optimal error estimate in the L2-norm and stability of the proposed scheme are proven, requiring that the time step is smaller than a given constant. Numerical results are provided to confirm the theoretical analysis and to demonstrate the potential blow-up behavior.

Keywords: Landau–Lifshitz equation; Lumped mass finite element; Optimal error estimate; Stability; Lagrange multiplier (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:220-235

DOI: 10.1016/j.matcom.2025.08.025

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