{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:25AXG6VH73SM7PLS7G5U4D62X5","short_pith_number":"pith:25AXG6VH","schema_version":"1.0","canonical_sha256":"d741737aa7fee4cfbd72f9bb4e0fdabf63013a481c3f2630a2fe9e9b29636c59","source":{"kind":"arxiv","id":"1606.05631","version":4},"attestation_state":"computed","paper":{"title":"Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dietmar Gallistl","submitted_at":"2016-06-17T19:38:59Z","abstract_excerpt":"This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \\& S\\\"uli [SIAM J.\\ Numer.\\ Anal.\\ 51(2013), pp.\\ 2088--2106.], and the second one is a new symmetric formulation based on a least-squares functional. These formulations enable the use of standard finite element techniques for variational problems in subspaces of $H^2$ as well as mixed finite element methods from the context of fluid computations. Besides the immediate quasi-optimal a~priori e"},"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":"1606.05631","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-17T19:38:59Z","cross_cats_sorted":[],"title_canon_sha256":"34a71acb67ade758d4a246adf81856b37d54730115bd77db7feda3c320df6c47","abstract_canon_sha256":"620a240684d902b403bddc474997e6a8704a15223cedf8b3b91d183993b3e832"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:50.080833Z","signature_b64":"M7D878Ue//Th7syvdx81M26zvlAMtLZ27BRM52n2eUsyNFmg/YU78PIMpH3hMzhhptfkPyrIDU5suvrilT1PCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d741737aa7fee4cfbd72f9bb4e0fdabf63013a481c3f2630a2fe9e9b29636c59","last_reissued_at":"2026-05-18T00:52:50.080101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:50.080101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dietmar Gallistl","submitted_at":"2016-06-17T19:38:59Z","abstract_excerpt":"This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \\& S\\\"uli [SIAM J.\\ Numer.\\ Anal.\\ 51(2013), pp.\\ 2088--2106.], and the second one is a new symmetric formulation based on a least-squares functional. These formulations enable the use of standard finite element techniques for variational problems in subspaces of $H^2$ as well as mixed finite element methods from the context of fluid computations. Besides the immediate quasi-optimal a~priori e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05631","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":""},"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":"1606.05631","created_at":"2026-05-18T00:52:50.080222+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.05631v4","created_at":"2026-05-18T00:52:50.080222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05631","created_at":"2026-05-18T00:52:50.080222+00:00"},{"alias_kind":"pith_short_12","alias_value":"25AXG6VH73SM","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"25AXG6VH73SM7PLS","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"25AXG6VH","created_at":"2026-05-18T12:29:52.810259+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/25AXG6VH73SM7PLS7G5U4D62X5","json":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5.json","graph_json":"https://pith.science/api/pith-number/25AXG6VH73SM7PLS7G5U4D62X5/graph.json","events_json":"https://pith.science/api/pith-number/25AXG6VH73SM7PLS7G5U4D62X5/events.json","paper":"https://pith.science/paper/25AXG6VH"},"agent_actions":{"view_html":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5","download_json":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5.json","view_paper":"https://pith.science/paper/25AXG6VH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.05631&json=true","fetch_graph":"https://pith.science/api/pith-number/25AXG6VH73SM7PLS7G5U4D62X5/graph.json","fetch_events":"https://pith.science/api/pith-number/25AXG6VH73SM7PLS7G5U4D62X5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5/action/storage_attestation","attest_author":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5/action/author_attestation","sign_citation":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5/action/citation_signature","submit_replication":"https://pith.science/pith/25AXG6VH73SM7PLS7G5U4D62X5/action/replication_record"}},"created_at":"2026-05-18T00:52:50.080222+00:00","updated_at":"2026-05-18T00:52:50.080222+00:00"}