BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates
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arXiv
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| Format: | Preprint |
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2026
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| author | Aldé, Michele Praetorius, Dirk Feischl, Michael |
| author_facet | Aldé, Michele Praetorius, Dirk Feischl, Michael |
| contents | We consider the Landau-Lifshitz-Gilbert equation (LLG), which models time-dependent micromagnetic phenomena. We analyze a fully discrete scheme that combines first-order finite elements in space with a BDF2 method in time. The method requires the solution of only one linear system of equations per time step and does not enforce the pointwise unit-length constraint of the magnetization. While unconditional weak convergence has been analyzed in an earlier work, we now prove optimal-order convergence rates under sufficient regularity assumptions on the exact solution and the external field. In combination with our previous work, this establishes the first higher-order-in-time and linear integrator that converges both to weak and strong solutions of LLG. Numerical experiments confirm first-order convergence in space and second-order convergence in time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates Aldé, Michele Praetorius, Dirk Feischl, Michael Numerical Analysis 65M12, 65M15 (Primary), 35K60, 65M60, 65L06, 65Z05 (Secondary) We consider the Landau-Lifshitz-Gilbert equation (LLG), which models time-dependent micromagnetic phenomena. We analyze a fully discrete scheme that combines first-order finite elements in space with a BDF2 method in time. The method requires the solution of only one linear system of equations per time step and does not enforce the pointwise unit-length constraint of the magnetization. While unconditional weak convergence has been analyzed in an earlier work, we now prove optimal-order convergence rates under sufficient regularity assumptions on the exact solution and the external field. In combination with our previous work, this establishes the first higher-order-in-time and linear integrator that converges both to weak and strong solutions of LLG. Numerical experiments confirm first-order convergence in space and second-order convergence in time. |
| title | BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates |
| topic | Numerical Analysis 65M12, 65M15 (Primary), 35K60, 65M60, 65L06, 65Z05 (Secondary) |
| url | https://arxiv.org/abs/2605.05129 |