Pith Number

pith:T322CL2V

pith:2026:T322CL2VD256FXV3AL75QBZZTX

not attested not anchored not stored refs pending

A Mixed Finite Element Method for the Dirichlet Vector Laplacian in Three Dimensions

Peiyang Yu, Ralf Hiptmair, Tianwei Yu

Mixed finite element method establishes well-posedness for the three-dimensional Dirichlet vector Laplacian via a non-standard vorticity space.

arxiv:2603.14026 v3 · 2026-03-14 · math.NA · cs.NA

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\pithnumber{T322CL2VD256FXV3AL75QBZZTX}

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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

This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition.

C2weakest assumption

The discrete Caccioppoli-type inequality for discrete curl-harmonic functions holds in the chosen finite element spaces on general three-dimensional domains.

C3one line summary

A mixed FEEC finite element approximation for the 3D Dirichlet vector Laplacian is well-posed, achieving (k-1/2)-order convergence in the energy norm on general domains and k-order convergence in L2 on convex domains for polynomial degree k.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T01:05:06.956563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ef5a12f551ebbe2debb02ffd807399dd861447c2af2d4140ef9765eb5f00479

Aliases

arxiv: 2603.14026 · arxiv_version: 2603.14026v3 · doi: 10.48550/arxiv.2603.14026 · pith_short_12: T322CL2VD256 · pith_short_16: T322CL2VD256FXV3 · pith_short_8: T322CL2V

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T322CL2VD256FXV3AL75QBZZTX \
  | 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: 9ef5a12f551ebbe2debb02ffd807399dd861447c2af2d4140ef9765eb5f00479

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42e22666d60d932d7cd392d86480727f3946b7c9f9f0cce86e72c0a2635c83f7",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-03-14T16:57:50Z",
    "title_canon_sha256": "aab751915e86ab70c8ff1a58c8011f2bd7bd37b402f4112f57b2b54e27ffdcd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.14026",
    "kind": "arxiv",
    "version": 3
  }
}