{"paper":{"title":"Mesh-Intrinsic GFEM: Asymptotic Smoothness on C^0 Unstructured Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Local polynomial reconstructions on overlapping patches blended by partition of unity cancel derivative jumps exactly for polynomials on standard C0 meshes.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Rong Tian","submitted_at":"2026-04-25T05:58:21Z","abstract_excerpt":"MiGFEM constructs enriched local approximations from the original nodal degrees of freedom of a finite element mesh, without extra enrichment unknowns, thereby avoiding the linear dependence, ill-conditioning, energy inconsistency, and mass-lumping difficulties of conventional enriched formulations.\n  This paper establishes asymptotic smoothness of MiGFEM on standard C0 unstructured meshes. Although the global approximation uses C0 partition-of-unity functions, its inter-element derivative jumps of order up to p decay as O(h^{p+1-|alpha|}) for solutions in C^{p+1}, and vanish identically when "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The core analysis establishes a partition-of-zero (PoZ) smoothness-transfer mechanism driven by interface coherence: derivative jumps cancel exactly for polynomial reproduction and decay as O(h^{p+1-||α||}) for smooth nonpolynomial fields.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That local polynomial reconstructions on overlapping nodal patches, when blended by partition of unity, produce interface coherence sufficient for exact derivative-jump cancellation on polynomials and the stated decay rate on non-polynomials, without additional global constraints or post-processing.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MiGFEM introduces a partition-of-zero smoothness-transfer mechanism that cancels derivative jumps exactly for polynomials and decays appropriately for smooth fields, enabling polynomial-exact intrinsic derivatives on C0 meshes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Local polynomial reconstructions on overlapping patches blended by partition of unity cancel derivative jumps exactly for polynomials on standard C0 meshes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d84f0ad31c116a60525cc9740c141c2e69bea8229038a0bba814b1b26ad9f688"},"source":{"id":"2604.23155","kind":"arxiv","version":2},"verdict":{"id":"b673fc9e-7e44-45c8-a04c-296df920d3ab","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T07:45:57.466907Z","strongest_claim":"The core analysis establishes a partition-of-zero (PoZ) smoothness-transfer mechanism driven by interface coherence: derivative jumps cancel exactly for polynomial reproduction and decay as O(h^{p+1-||α||}) for smooth nonpolynomial fields.","one_line_summary":"MiGFEM introduces a partition-of-zero smoothness-transfer mechanism that cancels derivative jumps exactly for polynomials and decays appropriately for smooth fields, enabling polynomial-exact intrinsic derivatives on C0 meshes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That local polynomial reconstructions on overlapping nodal patches, when blended by partition of unity, produce interface coherence sufficient for exact derivative-jump cancellation on polynomials and the stated decay rate on non-polynomials, without additional global constraints or post-processing.","pith_extraction_headline":"Local polynomial reconstructions on overlapping patches blended by partition of unity cancel derivative jumps exactly for polynomials on standard C0 meshes."},"integrity":{"clean":false,"summary":{"advisory":0,"critical":2,"by_detector":{"doi_compliance":{"total":2,"advisory":0,"critical":2,"informational":0}},"informational":0},"endpoint":"/pith/2604.23155/integrity.json","findings":[{"note":"Identifier '10.1007/s00466-017-1414-1' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","detector":"doi_compliance","severity":"critical","ref_index":28,"audited_at":"2026-05-19T23:24:36.471772Z","detected_doi":"10.1007/s00466-017-1414-1","finding_type":"unresolvable_identifier","verdict_class":"cross_source","detected_arxiv_id":null},{"note":"Identifier '10.1016/0898-1221(90)90109-6' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","detector":"doi_compliance","severity":"critical","ref_index":31,"audited_at":"2026-05-19T23:24:36.471772Z","detected_doi":"10.1016/0898-1221(90)90109-6","finding_type":"unresolvable_identifier","verdict_class":"cross_source","detected_arxiv_id":null}],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T09:38:48.028941Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:24:36.471772Z","status":"completed","version":"1.0.0","findings_count":2}],"snapshot_sha256":"218fdc007501b2fe79173cbb42baea530ecf4dba8a577bfb8a7fdf642ca7e53d"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}