Pith Number

pith:CZXJM5UG

pith:2026:CZXJM5UGFPBVZY3OGDGRYIXWZP

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Robust approximation error estimates for analysis-suitable $G^1$ isogeometric multi-patch discretizations

Fatima Hasanova, Stefan Takacs, Thomas Takacs

Analysis-suitable G1 multi-patch domains yield approximation errors independent of spline degree p for H2-conforming isogeometric discretizations.

arxiv:2605.13270 v1 · 2026-05-13 · math.NA · cs.NA

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Claims

C1strongest claim

We prove p-robust approximation error estimates for H²-conforming isogeometric discretizations over planar multi-patch domains... The resulting bounds on the approximation error depend on the geometry parameterization and on the Sobolev regularity of the target function, but are independent of the spline degree p.

C2weakest assumption

We restrict ourselves to the class of analysis-suitable G¹ (AS-G¹) multi-patch domains, which is the subset of C⁰-matching multi-patch domains that allows the definition of spline spaces that yield the necessary reproduction properties without the need to locally increase the degree.

C3one line summary

p-robust error bounds are established for H²-conforming C¹-smooth isogeometric spaces on AS-G¹ multi-patch domains, independent of polynomial degree p.

References

75 extracted · 75 resolved · 0 Pith anchors

[1] R. A. Adams and J. J. F. Fournier,Sobolev Spaces(Elsevier, 2003) 2003

[2] J. H. Argyris, I. Fried and D. W. Scharpf, The TUBA family of plate elements for the matrix displacement method,The Aeronautical Journal72(1968) 701–709 1968

[3] Y. Bazilevs, L. Beir˜ ao da Veiga, J. A. Cottrell, T. J. R. Hughes and G. Sangalli, Iso- geometric analysis: Approximation, stability and error estimates forh-refined meshes, Mathematical Models and M 2006

[4] Beir˜ ao da Veiga, A 2011

[5] A. Benvenuti, G. Loli, G. Sangalli and T. Takacs, Isogeometric multi-patchC 1-mortar coupling for the biharmonic equation,arXiv preprint arXiv:2303.07255

Formal links

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Receipt and verification

First computed	2026-05-18T02:44:49.282820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

166e9676862bc35ce36e30cd1c22f6cbdee65db6325fbb15ad5a7d65e7b917b4

Aliases

arxiv: 2605.13270 · arxiv_version: 2605.13270v1 · doi: 10.48550/arxiv.2605.13270 · pith_short_12: CZXJM5UGFPBV · pith_short_16: CZXJM5UGFPBVZY3O · pith_short_8: CZXJM5UG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CZXJM5UGFPBVZY3OGDGRYIXWZP \
  | 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: 166e9676862bc35ce36e30cd1c22f6cbdee65db6325fbb15ad5a7d65e7b917b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8e3532cea273201b3640412ad5b8696f1427040fe8555a7cda60cf97ed08d1b",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T09:48:57Z",
    "title_canon_sha256": "2fdbbb0f5c01cef187ac799cb50bcfd740cd6f8b2db4c4fd37034c5587b2700e"
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  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}