{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:Q42PYQ3FUZZQGTFERTZCEAO5CD","short_pith_number":"pith:Q42PYQ3F","schema_version":"1.0","canonical_sha256":"8734fc4365a673034ca48cf22201dd10c70d1eba1601f37d5332a51ce23f7d54","source":{"kind":"arxiv","id":"2401.15470","version":1},"attestation_state":"computed","paper":{"title":"Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"X.J. Wang, X.P. Xie","submitted_at":"2024-01-27T17:46:29Z","abstract_excerpt":"This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\\ (m\\geq1)$ and $m-1$ respectively for the approximations of velocity and pressure variables inside the elements and piecewise polynomials of degrees $k \\ ( k=m-1,m)$ and $m$ respectively for their numerical traces on the interfaces of elements, and are shown to yield globally divergence-free velocity approximation. Existence and uniqueness results for the discrete schemes, as well as optimal a priori error"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2401.15470","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-27T17:46:29Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c2ffee3bc85b33cc466564780b6a89ab9d377b109849b39787cc6578498179d4","abstract_canon_sha256":"31a8a9ac16e2194998d0cdcf6304b0a7f9d8ffe427b0297c18f099443af23a1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:38:16.600885Z","signature_b64":"lftwDHxtghBAU2N1mGZCRMTicwQeT8L0M+r1rEPnYIFJeVhwZ8cC/bZwFDFNQJFhTwO8cppPpdVr54uFfl1xBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8734fc4365a673034ca48cf22201dd10c70d1eba1601f37d5332a51ce23f7d54","last_reissued_at":"2026-07-05T07:38:16.600399Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:38:16.600399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Robust globally divergence-free weak Galerkin methods for stationary incompressible convective Brinkman-Forchheimer equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"X.J. Wang, X.P. Xie","submitted_at":"2024-01-27T17:46:29Z","abstract_excerpt":"This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\\ (m\\geq1)$ and $m-1$ respectively for the approximations of velocity and pressure variables inside the elements and piecewise polynomials of degrees $k \\ ( k=m-1,m)$ and $m$ respectively for their numerical traces on the interfaces of elements, and are shown to yield globally divergence-free velocity approximation. Existence and uniqueness results for the discrete schemes, as well as optimal a priori error"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15470","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.15470/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2401.15470","created_at":"2026-07-05T07:38:16.600458+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.15470v1","created_at":"2026-07-05T07:38:16.600458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.15470","created_at":"2026-07-05T07:38:16.600458+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q42PYQ3FUZZQ","created_at":"2026-07-05T07:38:16.600458+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q42PYQ3FUZZQGTFE","created_at":"2026-07-05T07:38:16.600458+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q42PYQ3F","created_at":"2026-07-05T07:38:16.600458+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD","json":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD.json","graph_json":"https://pith.science/api/pith-number/Q42PYQ3FUZZQGTFERTZCEAO5CD/graph.json","events_json":"https://pith.science/api/pith-number/Q42PYQ3FUZZQGTFERTZCEAO5CD/events.json","paper":"https://pith.science/paper/Q42PYQ3F"},"agent_actions":{"view_html":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD","download_json":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD.json","view_paper":"https://pith.science/paper/Q42PYQ3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.15470&json=true","fetch_graph":"https://pith.science/api/pith-number/Q42PYQ3FUZZQGTFERTZCEAO5CD/graph.json","fetch_events":"https://pith.science/api/pith-number/Q42PYQ3FUZZQGTFERTZCEAO5CD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD/action/storage_attestation","attest_author":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD/action/author_attestation","sign_citation":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD/action/citation_signature","submit_replication":"https://pith.science/pith/Q42PYQ3FUZZQGTFERTZCEAO5CD/action/replication_record"}},"created_at":"2026-07-05T07:38:16.600458+00:00","updated_at":"2026-07-05T07:38:16.600458+00:00"}