{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I","short_pith_number":"pith:VT5YOSF5","schema_version":"1.0","canonical_sha256":"acfb8748bd4ff22e4eeb0ff3cc8d90fa1ca9eece576157c9f6ff409d8d72b36f","source":{"kind":"arxiv","id":"1307.7578","version":1},"attestation_state":"computed","paper":{"title":"Optimal error estimate for semi-implicit space-time discretization for the equations describing incompressible generalized Newtonian fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lars Diening, Luigi C. Berselli, Michael Ruzicka","submitted_at":"2013-07-29T13:47:04Z","abstract_excerpt":"In this paper we study the numerical error arising in the space-time approximation of unsteady generalized Newtonian fluids which possess a stress-tensor with $(p,\\delta)$-structure. A semi-implicit time-discretization scheme coupled with conforming inf-sup stable finite element space discretization is analyzed. The main result, which improves previous suboptimal estimates as those in [A. Prohl, and M. Ruzicka, SIAM J. Numer. Anal., 39 (2001), pp. 214--249] is the optimal $O(k+h)$ error-estimate valid in the range $p\\in (3/2,2]$, where $k$ and $h$ are the time-step and the mesh-size, respectiv"},"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":"1307.7578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-07-29T13:47:04Z","cross_cats_sorted":[],"title_canon_sha256":"2d8f14c7c53e1128520379bcca6671b88b360f845691e3c6cdebe4569a1c4aca","abstract_canon_sha256":"d8cf5b2d94ccdaa6a0ac3c817b64a247cf3f7c82adda4b5a0cede9b50bb1a1b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:22.925534Z","signature_b64":"TCqI5ciclguYJVNm3fPOVtVX7EzPocHGpkJ/wlVxwq9PFT/MaV2hylon69xw8RvEPRalaZjC1sR8gpN7kG46BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acfb8748bd4ff22e4eeb0ff3cc8d90fa1ca9eece576157c9f6ff409d8d72b36f","last_reissued_at":"2026-05-18T03:17:22.924761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:22.924761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal error estimate for semi-implicit space-time discretization for the equations describing incompressible generalized Newtonian fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lars Diening, Luigi C. Berselli, Michael Ruzicka","submitted_at":"2013-07-29T13:47:04Z","abstract_excerpt":"In this paper we study the numerical error arising in the space-time approximation of unsteady generalized Newtonian fluids which possess a stress-tensor with $(p,\\delta)$-structure. A semi-implicit time-discretization scheme coupled with conforming inf-sup stable finite element space discretization is analyzed. The main result, which improves previous suboptimal estimates as those in [A. Prohl, and M. Ruzicka, SIAM J. Numer. Anal., 39 (2001), pp. 214--249] is the optimal $O(k+h)$ error-estimate valid in the range $p\\in (3/2,2]$, where $k$ and $h$ are the time-step and the mesh-size, respectiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7578","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":"1307.7578","created_at":"2026-05-18T03:17:22.924885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.7578v1","created_at":"2026-05-18T03:17:22.924885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7578","created_at":"2026-05-18T03:17:22.924885+00:00"},{"alias_kind":"pith_short_12","alias_value":"VT5YOSF5J7ZC","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VT5YOSF5J7ZC4TXL","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VT5YOSF5","created_at":"2026-05-18T12:28:04.890932+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/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I","json":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I.json","graph_json":"https://pith.science/api/pith-number/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/graph.json","events_json":"https://pith.science/api/pith-number/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/events.json","paper":"https://pith.science/paper/VT5YOSF5"},"agent_actions":{"view_html":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I","download_json":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I.json","view_paper":"https://pith.science/paper/VT5YOSF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.7578&json=true","fetch_graph":"https://pith.science/api/pith-number/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/graph.json","fetch_events":"https://pith.science/api/pith-number/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/action/storage_attestation","attest_author":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/action/author_attestation","sign_citation":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/action/citation_signature","submit_replication":"https://pith.science/pith/VT5YOSF5J7ZC4TXLB7Z4ZDMQ7I/action/replication_record"}},"created_at":"2026-05-18T03:17:22.924885+00:00","updated_at":"2026-05-18T03:17:22.924885+00:00"}