{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CDF42SXONONT6GH6VDUAALGVKN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"11af38402206a2d1fc9b0533ef9bc3a3839b197e8e0a9a7ac1afa369fa56d220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-28T09:08:27Z","title_canon_sha256":"650987a999e77399758c47e3f85db888a8442460d915dbca99bae5428ccfdea1"},"schema_version":"1.0","source":{"id":"1808.09185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09185","created_at":"2026-05-18T00:07:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09185v1","created_at":"2026-05-18T00:07:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09185","created_at":"2026-05-18T00:07:02Z"},{"alias_kind":"pith_short_12","alias_value":"CDF42SXONONT","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CDF42SXONONT6GH6","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CDF42SXO","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:47efcca40fe6b6ab9acfc9bf985476c83fdbed9b60692bf4fe8519f03c36a811","target":"graph","created_at":"2026-05-18T00:07:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse and a fine one. The main computational effort is done on the coarsest velocity space with an implicit and unconditionally time scheme while its correction on the finer velocity space is realized with a simple stabilized semi-implicit scheme whose the lack of stability is compensated by a high mode stabilization procedure; the pressure is updated using the free","authors_text":"Clara Al Kosseifi, Hyam Abboud, Jean-Paul Chehab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-28T09:08:27Z","title":"Stabilized bi-grid projection methods in Finite Elements for the 2D incompressible Navier-Stokes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09185","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3f87c00edd990dcff0c281f525019ba9988876c0f76df4f83535e609e524b6d7","target":"record","created_at":"2026-05-18T00:07:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"11af38402206a2d1fc9b0533ef9bc3a3839b197e8e0a9a7ac1afa369fa56d220","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-08-28T09:08:27Z","title_canon_sha256":"650987a999e77399758c47e3f85db888a8442460d915dbca99bae5428ccfdea1"},"schema_version":"1.0","source":{"id":"1808.09185","kind":"arxiv","version":1}},"canonical_sha256":"10cbcd4aee6b9b3f18fea8e8002cd5534751e7a8b2679cfa231cdbca4bf3beb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10cbcd4aee6b9b3f18fea8e8002cd5534751e7a8b2679cfa231cdbca4bf3beb0","first_computed_at":"2026-05-18T00:07:02.072158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:02.072158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SFLT0I/2c02TeSDbpUJKE+IyoPN/6Gjc/i8ZBC7iQRmMbupQILPAOpJG5CkEw9eJP4DWtHVbjYU0taLGT2WQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:02.072671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f87c00edd990dcff0c281f525019ba9988876c0f76df4f83535e609e524b6d7","sha256:47efcca40fe6b6ab9acfc9bf985476c83fdbed9b60692bf4fe8519f03c36a811"],"state_sha256":"796dcad060bcbee787c72276dccfa777d83076860ae350a493ce03a4e6ca1ddb"}