{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HEJLT6PRI6WQUHMPBI3XAGWS53","short_pith_number":"pith:HEJLT6PR","schema_version":"1.0","canonical_sha256":"3912b9f9f147ad0a1d8f0a37701ad2eefc336ebcd380693e59f0369a1c143ad1","source":{"kind":"arxiv","id":"1709.03063","version":2},"attestation_state":"computed","paper":{"title":"Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Alexander Linke, Christoph Lehrenfeld, Gert Lube, Philipp W. Schroeder","submitted_at":"2017-09-10T07:45:00Z","abstract_excerpt":"Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, $Re$-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on "},"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":"1709.03063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-10T07:45:00Z","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph","physics.flu-dyn"],"title_canon_sha256":"0f5d94263bded495cd609e8ae1670051fbca1cf076edc2c88e14e6c16b05981d","abstract_canon_sha256":"2167dacb5686fc540aa7ddd7201d616ce678a0e68f2de5f5c2ac2270a53f6588"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:53.112561Z","signature_b64":"CCPq4hQRrwVaer3oNeznNWCfGOCytmRPpLRKDGuGV6r2TVzcUaol+U3XuFtbRWwOJgflFZBcf5dWqvXEw9zgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3912b9f9f147ad0a1d8f0a37701ad2eefc336ebcd380693e59f0369a1c143ad1","last_reissued_at":"2026-05-17T23:48:53.112108Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:53.112108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.comp-ph","physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Alexander Linke, Christoph Lehrenfeld, Gert Lube, Philipp W. Schroeder","submitted_at":"2017-09-10T07:45:00Z","abstract_excerpt":"Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, $Re$-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03063","kind":"arxiv","version":2},"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":"1709.03063","created_at":"2026-05-17T23:48:53.112174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03063v2","created_at":"2026-05-17T23:48:53.112174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03063","created_at":"2026-05-17T23:48:53.112174+00:00"},{"alias_kind":"pith_short_12","alias_value":"HEJLT6PRI6WQ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HEJLT6PRI6WQUHMP","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HEJLT6PR","created_at":"2026-05-18T12:31:18.294218+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/HEJLT6PRI6WQUHMPBI3XAGWS53","json":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53.json","graph_json":"https://pith.science/api/pith-number/HEJLT6PRI6WQUHMPBI3XAGWS53/graph.json","events_json":"https://pith.science/api/pith-number/HEJLT6PRI6WQUHMPBI3XAGWS53/events.json","paper":"https://pith.science/paper/HEJLT6PR"},"agent_actions":{"view_html":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53","download_json":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53.json","view_paper":"https://pith.science/paper/HEJLT6PR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03063&json=true","fetch_graph":"https://pith.science/api/pith-number/HEJLT6PRI6WQUHMPBI3XAGWS53/graph.json","fetch_events":"https://pith.science/api/pith-number/HEJLT6PRI6WQUHMPBI3XAGWS53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53/action/storage_attestation","attest_author":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53/action/author_attestation","sign_citation":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53/action/citation_signature","submit_replication":"https://pith.science/pith/HEJLT6PRI6WQUHMPBI3XAGWS53/action/replication_record"}},"created_at":"2026-05-17T23:48:53.112174+00:00","updated_at":"2026-05-17T23:48:53.112174+00:00"}