{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KGEGMPAPCVKPWJF5KXRMOXYPF5","short_pith_number":"pith:KGEGMPAP","schema_version":"1.0","canonical_sha256":"5188663c0f1554fb24bd55e2c75f0f2f6e52d2d2e5086d76d0afcb6533c5d9ca","source":{"kind":"arxiv","id":"1312.1313","version":3},"attestation_state":"computed","paper":{"title":"Analysis of a Mixed Finite Element Method for a Cahn-Hilliard-Darcy-Stokes System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amanda E. Diegel, Steven M. Wise, Xiaobing H. Feng","submitted_at":"2013-12-04T20:20:02Z","abstract_excerpt":"In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock copolymer melts. The time discretization is based on a convex splitting of the energy of the equation. We prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system and unconditionally uniquely solvable. We prove that the phase variable is bounded in $L^\\infty \\left(0,T,L^\\"},"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":"1312.1313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-04T20:20:02Z","cross_cats_sorted":[],"title_canon_sha256":"3c9c87fc800b4ec541e9dc1905e0c5452895cb32935157c2d3bb2d995d2c32cb","abstract_canon_sha256":"e1e6661f636742d8362282e14541ace2694db13836439ca214fb7d2f5c4f5040"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:06.115646Z","signature_b64":"Y7eYmYlJ4N6B3y5Za7UsarRvXPfyjGEllLrV/+qXQ4lvpYO4SClIGyXfHntwa5kbHbUnjdvBP7irrbh2wZ3pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5188663c0f1554fb24bd55e2c75f0f2f6e52d2d2e5086d76d0afcb6533c5d9ca","last_reissued_at":"2026-05-18T03:04:06.115134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:06.115134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of a Mixed Finite Element Method for a Cahn-Hilliard-Darcy-Stokes System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Amanda E. Diegel, Steven M. Wise, Xiaobing H. Feng","submitted_at":"2013-12-04T20:20:02Z","abstract_excerpt":"In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and coupled fluid flow in immiscible binary fluids and diblock copolymer melts. The time discretization is based on a convex splitting of the energy of the equation. We prove that our scheme is unconditionally energy stable with respect to a spatially discrete analogue of the continuous free energy of the system and unconditionally uniquely solvable. We prove that the phase variable is bounded in $L^\\infty \\left(0,T,L^\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1313","kind":"arxiv","version":3},"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":"1312.1313","created_at":"2026-05-18T03:04:06.115211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1313v3","created_at":"2026-05-18T03:04:06.115211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1313","created_at":"2026-05-18T03:04:06.115211+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGEGMPAPCVKP","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGEGMPAPCVKPWJF5","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGEGMPAP","created_at":"2026-05-18T12:27:49.015174+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/KGEGMPAPCVKPWJF5KXRMOXYPF5","json":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5.json","graph_json":"https://pith.science/api/pith-number/KGEGMPAPCVKPWJF5KXRMOXYPF5/graph.json","events_json":"https://pith.science/api/pith-number/KGEGMPAPCVKPWJF5KXRMOXYPF5/events.json","paper":"https://pith.science/paper/KGEGMPAP"},"agent_actions":{"view_html":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5","download_json":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5.json","view_paper":"https://pith.science/paper/KGEGMPAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1313&json=true","fetch_graph":"https://pith.science/api/pith-number/KGEGMPAPCVKPWJF5KXRMOXYPF5/graph.json","fetch_events":"https://pith.science/api/pith-number/KGEGMPAPCVKPWJF5KXRMOXYPF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5/action/storage_attestation","attest_author":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5/action/author_attestation","sign_citation":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5/action/citation_signature","submit_replication":"https://pith.science/pith/KGEGMPAPCVKPWJF5KXRMOXYPF5/action/replication_record"}},"created_at":"2026-05-18T03:04:06.115211+00:00","updated_at":"2026-05-18T03:04:06.115211+00:00"}