{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OPVCD3UWDJB4O3EKIQD3ES43M5","short_pith_number":"pith:OPVCD3UW","schema_version":"1.0","canonical_sha256":"73ea21ee961a43c76c8a4407b24b9b675afe1b05b52b60f208a1c78ba62229de","source":{"kind":"arxiv","id":"1204.2145","version":3},"attestation_state":"computed","paper":{"title":"Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Kreuzer, Endre S\\\"uli, Lars Diening","submitted_at":"2012-04-10T13:39:15Z","abstract_excerpt":"We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi--valued, maximal monotone $r$-graph, with $1<r<\\infty$. Using a variety of weak compactness techniques, including Chacon's biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to 0"},"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":"1204.2145","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-10T13:39:15Z","cross_cats_sorted":[],"title_canon_sha256":"f735989c3b69647d74848e692b1e38b08edf1761fa6ec8a1e8d2e0ab2f2be200","abstract_canon_sha256":"cc1709c28b7a74a0b6ead89efaa26e43a0c6497bbb502be390af1c76b0f99e31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:38.546823Z","signature_b64":"hcJ+kBnEltIeouDSlf7v4SLt9N4jwYfooRY8iRWJPeYToPrHmW6l+U4n50G4v/A00EprnNSU0QBPkY3dUtE/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73ea21ee961a43c76c8a4407b24b9b675afe1b05b52b60f208a1c78ba62229de","last_reissued_at":"2026-05-18T03:08:38.546171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:38.546171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Kreuzer, Endre S\\\"uli, Lars Diening","submitted_at":"2012-04-10T13:39:15Z","abstract_excerpt":"We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi--valued, maximal monotone $r$-graph, with $1<r<\\infty$. Using a variety of weak compactness techniques, including Chacon's biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to 0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2145","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":"1204.2145","created_at":"2026-05-18T03:08:38.546257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2145v3","created_at":"2026-05-18T03:08:38.546257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2145","created_at":"2026-05-18T03:08:38.546257+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPVCD3UWDJB4","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPVCD3UWDJB4O3EK","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPVCD3UW","created_at":"2026-05-18T12:27:16.716162+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/OPVCD3UWDJB4O3EKIQD3ES43M5","json":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5.json","graph_json":"https://pith.science/api/pith-number/OPVCD3UWDJB4O3EKIQD3ES43M5/graph.json","events_json":"https://pith.science/api/pith-number/OPVCD3UWDJB4O3EKIQD3ES43M5/events.json","paper":"https://pith.science/paper/OPVCD3UW"},"agent_actions":{"view_html":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5","download_json":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5.json","view_paper":"https://pith.science/paper/OPVCD3UW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2145&json=true","fetch_graph":"https://pith.science/api/pith-number/OPVCD3UWDJB4O3EKIQD3ES43M5/graph.json","fetch_events":"https://pith.science/api/pith-number/OPVCD3UWDJB4O3EKIQD3ES43M5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5/action/storage_attestation","attest_author":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5/action/author_attestation","sign_citation":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5/action/citation_signature","submit_replication":"https://pith.science/pith/OPVCD3UWDJB4O3EKIQD3ES43M5/action/replication_record"}},"created_at":"2026-05-18T03:08:38.546257+00:00","updated_at":"2026-05-18T03:08:38.546257+00:00"}