{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UPZ6TWBBZ3Y77MZP24WMSDHNW3","short_pith_number":"pith:UPZ6TWBB","schema_version":"1.0","canonical_sha256":"a3f3e9d821cef1ffb32fd72cc90cedb6e751453ed0bb136143a858cc6862922f","source":{"kind":"arxiv","id":"2508.06235","version":4},"attestation_state":"computed","paper":{"title":"Fully discrete error analysis of finite element discretizations of time-dependent Stokes equations in a stream-function formulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Boris Vexler, Dmitriy Leykekhman, Jakob Wagner","submitted_at":"2025-08-08T11:38:01Z","abstract_excerpt":"In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous Galerkin method of arbitrary degree, whereas we present the space discretization in a general framework. This makes our result applicable for a wide variety of space discretization methods, provided some Galerkin orthogonality conditions are satisfied. As an example, conformal $C^1$ and $C^0$ interior penalty methods are covered by our analysis. The results do"},"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":"2508.06235","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-08-08T11:38:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"610b1a5897bbb08a0505e78552f42942a380b59234e23f7b8240fac8b772ae63","abstract_canon_sha256":"86c9dd4e66ad07ee1e055425b3486084716b3fe2fd3687be2ae8babdd86f5766"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:04:56.550079Z","signature_b64":"hsLL4cKhC7Nc+60BYHRxl9AuIQfJEaFI5b38SOxYg+M5nJk8H4F5ibMnRDeypXQMem+G50H89vub628Z+BQZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3f3e9d821cef1ffb32fd72cc90cedb6e751453ed0bb136143a858cc6862922f","last_reissued_at":"2026-05-20T01:04:56.549207Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:04:56.549207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fully discrete error analysis of finite element discretizations of time-dependent Stokes equations in a stream-function formulation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Boris Vexler, Dmitriy Leykekhman, Jakob Wagner","submitted_at":"2025-08-08T11:38:01Z","abstract_excerpt":"In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous Galerkin method of arbitrary degree, whereas we present the space discretization in a general framework. This makes our result applicable for a wide variety of space discretization methods, provided some Galerkin orthogonality conditions are satisfied. As an example, conformal $C^1$ and $C^0$ interior penalty methods are covered by our analysis. The results do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.06235","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.06235/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2508.06235","created_at":"2026-05-20T01:04:56.549338+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.06235v4","created_at":"2026-05-20T01:04:56.549338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.06235","created_at":"2026-05-20T01:04:56.549338+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPZ6TWBBZ3Y7","created_at":"2026-05-20T01:04:56.549338+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPZ6TWBBZ3Y77MZP","created_at":"2026-05-20T01:04:56.549338+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPZ6TWBB","created_at":"2026-05-20T01:04:56.549338+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/UPZ6TWBBZ3Y77MZP24WMSDHNW3","json":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3.json","graph_json":"https://pith.science/api/pith-number/UPZ6TWBBZ3Y77MZP24WMSDHNW3/graph.json","events_json":"https://pith.science/api/pith-number/UPZ6TWBBZ3Y77MZP24WMSDHNW3/events.json","paper":"https://pith.science/paper/UPZ6TWBB"},"agent_actions":{"view_html":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3","download_json":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3.json","view_paper":"https://pith.science/paper/UPZ6TWBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.06235&json=true","fetch_graph":"https://pith.science/api/pith-number/UPZ6TWBBZ3Y77MZP24WMSDHNW3/graph.json","fetch_events":"https://pith.science/api/pith-number/UPZ6TWBBZ3Y77MZP24WMSDHNW3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3/action/storage_attestation","attest_author":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3/action/author_attestation","sign_citation":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3/action/citation_signature","submit_replication":"https://pith.science/pith/UPZ6TWBBZ3Y77MZP24WMSDHNW3/action/replication_record"}},"created_at":"2026-05-20T01:04:56.549338+00:00","updated_at":"2026-05-20T01:04:56.549338+00:00"}