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

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  • Yang, Xingwei
  • Huang, Pengzhan
  • He, Yinnian

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.

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  • Yang, Xingwei & Huang, Pengzhan & He, Yinnian, 2026. "Optimal error estimate of a linearized FEM based on the Lagrange multiplier approach for the Landau–Lifshitz equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 220-235.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:220-235
    DOI: 10.1016/j.matcom.2025.08.025
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