{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZVZUVGTNF6AUX2ZTDPQU5GR4S2","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":"71114ac0790590745352b729e3582aa985bcb1c8f8e87d201ca4e03aa64b60a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-20T15:21:14Z","title_canon_sha256":"762a871745ff944f4cec44d8df48387e03770d61f8c794abfd440b2d1e63c0cd"},"schema_version":"1.0","source":{"id":"1712.08006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08006","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08006v1","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08006","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZVZUVGTNF6AU","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZVZUVGTNF6AUX2ZT","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZVZUVGTN","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:e4ecbdb79d3f7126d6884b1ef571f8138d766ea6fff4d9b83ab380add7c8bd0f","target":"graph","created_at":"2026-05-17T23:47:31Z","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":"The general theory of Babu\\v{s}ka ensures necessary and sufficient conditions for a mixed problem in classical or Petrov-Galerkin form to be well posed in the sense of Hadamard. Moreover, the mixed method of Raviart-Thomas with low-level elements can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of type Petrov-Galerkin to ensure a local computation of the gradient at the interfaces of the elements. The in-depth study of stability leads to a specific choice of the test functions. With this choice, we show on the one hand that the ","authors_text":"Charles Pierre (LMAP), Fran\\c{c}ois Dubois (LM-Orsay, Isabelle Greff (LMAP), LMSSC)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-20T15:21:14Z","title":"Raviart Thomas Petrov-Galerkin Finite Elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08006","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":"sha256:72363581d7e69d2e527b1c5817c7ac63e40bb652655cebdd3cbdc9b7459470fe","target":"record","created_at":"2026-05-17T23:47:31Z","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":"71114ac0790590745352b729e3582aa985bcb1c8f8e87d201ca4e03aa64b60a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-20T15:21:14Z","title_canon_sha256":"762a871745ff944f4cec44d8df48387e03770d61f8c794abfd440b2d1e63c0cd"},"schema_version":"1.0","source":{"id":"1712.08006","kind":"arxiv","version":1}},"canonical_sha256":"cd734a9a6d2f814beb331be14e9a3c96a3f8a274edcf59bd9a7333c3bf3c0e3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd734a9a6d2f814beb331be14e9a3c96a3f8a274edcf59bd9a7333c3bf3c0e3e","first_computed_at":"2026-05-17T23:47:31.646881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.646881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YW//2ylMdyV176uvxOOwUEQgtlFVqbYyPoOktl+oSfufhiZN8tfNMvSMmGI0ZNtUeoaJVOj3MSkEBmfb4zM9DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.647660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72363581d7e69d2e527b1c5817c7ac63e40bb652655cebdd3cbdc9b7459470fe","sha256:e4ecbdb79d3f7126d6884b1ef571f8138d766ea6fff4d9b83ab380add7c8bd0f"],"state_sha256":"5b54c7c5fabab6498209262722f9b9529fdc1a42a5e9a1c233bc0502ff994f41"}