{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7EQTIPUEMOBJCH7ZVL7XR6M6WC","short_pith_number":"pith:7EQTIPUE","schema_version":"1.0","canonical_sha256":"f921343e846382911ff9aaff78f99eb0a2416d5580dcf43cd7744a42e4acf89a","source":{"kind":"arxiv","id":"1606.02668","version":1},"attestation_state":"computed","paper":{"title":"Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amanda E. Diegel, Cheng Wang, Steven M. Wise, Xiaoming Wang","submitted_at":"2016-06-08T18:10:59Z","abstract_excerpt":"In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the Navier-Stokes equations and a modification to the Crank-Nicholson method for the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn-Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the"},"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":"1606.02668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-08T18:10:59Z","cross_cats_sorted":[],"title_canon_sha256":"ed014397d856ef2fa80c9879d49b74a25c5f5f1a12047ba1079b895c7c5df892","abstract_canon_sha256":"072f0c98ec766b9b772f63d6fefa5020bfa548a8b30c3e8a123d948f02809bcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:40.885216Z","signature_b64":"sNLstqHNlznwO/XbO0zNdX0m3ggXqSQYHCrNnXhtl4GQmsOBkA35/VPo4bje0zEFzClBp814UW7zy9yTGCjiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f921343e846382911ff9aaff78f99eb0a2416d5580dcf43cd7744a42e4acf89a","last_reissued_at":"2026-05-18T01:12:40.884829Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:40.884829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amanda E. Diegel, Cheng Wang, Steven M. Wise, Xiaoming Wang","submitted_at":"2016-06-08T18:10:59Z","abstract_excerpt":"In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the Navier-Stokes equations and a modification to the Crank-Nicholson method for the Cahn-Hilliard equation. In particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn-Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02668","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":""},"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":"1606.02668","created_at":"2026-05-18T01:12:40.884891+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02668v1","created_at":"2026-05-18T01:12:40.884891+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02668","created_at":"2026-05-18T01:12:40.884891+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EQTIPUEMOBJ","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EQTIPUEMOBJCH7Z","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EQTIPUE","created_at":"2026-05-18T12:30:04.600751+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/7EQTIPUEMOBJCH7ZVL7XR6M6WC","json":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC.json","graph_json":"https://pith.science/api/pith-number/7EQTIPUEMOBJCH7ZVL7XR6M6WC/graph.json","events_json":"https://pith.science/api/pith-number/7EQTIPUEMOBJCH7ZVL7XR6M6WC/events.json","paper":"https://pith.science/paper/7EQTIPUE"},"agent_actions":{"view_html":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC","download_json":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC.json","view_paper":"https://pith.science/paper/7EQTIPUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02668&json=true","fetch_graph":"https://pith.science/api/pith-number/7EQTIPUEMOBJCH7ZVL7XR6M6WC/graph.json","fetch_events":"https://pith.science/api/pith-number/7EQTIPUEMOBJCH7ZVL7XR6M6WC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC/action/storage_attestation","attest_author":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC/action/author_attestation","sign_citation":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC/action/citation_signature","submit_replication":"https://pith.science/pith/7EQTIPUEMOBJCH7ZVL7XR6M6WC/action/replication_record"}},"created_at":"2026-05-18T01:12:40.884891+00:00","updated_at":"2026-05-18T01:12:40.884891+00:00"}