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In co","authors_text":"Dirk Praetorius, Michael Feischl, Michele Ald\\'e","cross_cats":["cs.NA"],"headline":"A linear BDF2 scheme paired with finite elements achieves optimal-order convergence for the Landau-Lifshitz-Gilbert equation.","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-06T16:56:38Z","title":"BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.05129","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T15:49:24.570215Z","id":"0fe8a8cd-ec5e-46db-a672-562513c1d3fc","model_set":{"reader":"grok-4.3"},"one_line_summary":"A linear BDF2 finite-element integrator for the LLG equation achieves first-order spatial and second-order temporal convergence rates and converges to both weak and strong solutions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A linear BDF2 scheme paired with finite elements achieves optimal-order convergence for the Landau-Lifshitz-Gilbert equation.","strongest_claim":"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.","weakest_assumption":"Sufficient regularity assumptions on the exact solution and the external field are required for the optimal-order a-priori error estimates to hold."}},"verdict_id":"0fe8a8cd-ec5e-46db-a672-562513c1d3fc"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8cae580d06172c088e9ff5c3723f5a6f1a972da38e89989e0670d33745e42ec5","target":"record","created_at":"2026-07-01T01:17:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8f36588b2cfcfdd7837aff5437fef2f318da98a27a3597eac22779bc2c3207d8","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-06T16:56:38Z","title_canon_sha256":"cd2d2c49e047ee9d804a9257a709d30eccae1b876b3598b59554af527b512671"},"schema_version":"1.0","source":{"id":"2605.05129","kind":"arxiv","version":2}},"canonical_sha256":"7a2b30a9e71bb20d254586765930854173c321fdc4d371943cfe1b5582b089d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a2b30a9e71bb20d254586765930854173c321fdc4d371943cfe1b5582b089d0","first_computed_at":"2026-07-01T01:17:51.573391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:51.573391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqB+HWYkMV21pKl78FtpYlY53aLLchZ/z8oUTWc2LBRut9U56Ud/U0ULNU2hacyf6kF91eXB6MuQJUrj4rnoBg==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:51.573816Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.05129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b74d4883356522d0a800b9a146eca1a0545dfdbcd422b10f84a8e774fc3d5286","sha256:8cae580d06172c088e9ff5c3723f5a6f1a972da38e89989e0670d33745e42ec5","sha256:fe0a80c15a230dc1f974782f8a981a940513fcf7909305ee34b257bfe960c41a"],"state_sha256":"8f7282916a1a9fb76dacc73afafdad4405dd546b8fbc5abfd5eec50c57fee103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P3inokQSAfW293uGZHGKBeYSZXhq8aT9bMJAc+rGzUks07wCsLRoZUty+mfk12pGln6lGxk7rPejZgCyktNRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T18:23:40.284851Z","bundle_sha256":"e5332ab579231cf777abbefabd44dbb9446150f459a5cf6e35eff76a0774e090"}}