Pith Number

pith:PIVTBKPH

pith:2026:PIVTBKPHDOZA2JKFQZ3FSMEFIF

not attested not anchored not stored refs pending

BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics: a-priori error estimates

Dirk Praetorius, Michael Feischl, Michele Ald\'e

A linear BDF2 scheme paired with finite elements achieves optimal-order convergence for the Landau-Lifshitz-Gilbert equation.

arxiv:2605.05129 v2 · 2026-05-06 · math.NA · cs.NA

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\usepackage{pith}
\pithnumber{PIVTBKPHDOZA2JKFQZ3FSMEFIF}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest assumption

Sufficient regularity assumptions on the exact solution and the external field are required for the optimal-order a-priori error estimates to hold.

C3one 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.

Receipt and verification

First computed	2026-07-01T01:17:51.573391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a2b30a9e71bb20d254586765930854173c321fdc4d371943cfe1b5582b089d0

Aliases

arxiv: 2605.05129 · arxiv_version: 2605.05129v2 · doi: 10.48550/arxiv.2605.05129 · pith_short_12: PIVTBKPHDOZA · pith_short_16: PIVTBKPHDOZA2JKF · pith_short_8: PIVTBKPH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PIVTBKPHDOZA2JKFQZ3FSMEFIF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 7a2b30a9e71bb20d254586765930854173c321fdc4d371943cfe1b5582b089d0

Canonical record JSON

{
  "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
  }
}