{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SKR6DSJ75HZFDQGWFIPCOZNFME","short_pith_number":"pith:SKR6DSJ7","schema_version":"1.0","canonical_sha256":"92a3e1c93fe9f251c0d62a1e2765a561198cd24f6799d2ff46d8e2c409aa519d","source":{"kind":"arxiv","id":"1101.1218","version":1},"attestation_state":"computed","paper":{"title":"Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Li Wang, Xiaoping Xie","submitted_at":"2011-01-06T14:20:23Z","abstract_excerpt":"This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a $C^0$ extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results."},"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":"1101.1218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-06T14:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"273e14ab5e0b4d169a369d21992ec706d4b303ecab4782d189858a05a7684f82","abstract_canon_sha256":"13d0b1559b2b2ab8608782be81b411969c8d1d969eaff6eb271da7bd700fa548"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:00.308756Z","signature_b64":"KIgk4bHbeNBQx1anSQdFCoHwlY52DXx+EsbZIRUrjNsKJWzV2QGiiDJ2+r/ucVfXeDOn11alI/h9290bec8rAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a3e1c93fe9f251c0d62a1e2765a561198cd24f6799d2ff46d8e2c409aa519d","last_reissued_at":"2026-05-18T04:32:00.307995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:00.307995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Li Wang, Xiaoping Xie","submitted_at":"2011-01-06T14:20:23Z","abstract_excerpt":"This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a $C^0$ extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1218","kind":"arxiv","version":1},"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":"1101.1218","created_at":"2026-05-18T04:32:00.308110+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1218v1","created_at":"2026-05-18T04:32:00.308110+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1218","created_at":"2026-05-18T04:32:00.308110+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKR6DSJ75HZF","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKR6DSJ75HZFDQGW","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKR6DSJ7","created_at":"2026-05-18T12:26:41.206345+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/SKR6DSJ75HZFDQGWFIPCOZNFME","json":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME.json","graph_json":"https://pith.science/api/pith-number/SKR6DSJ75HZFDQGWFIPCOZNFME/graph.json","events_json":"https://pith.science/api/pith-number/SKR6DSJ75HZFDQGWFIPCOZNFME/events.json","paper":"https://pith.science/paper/SKR6DSJ7"},"agent_actions":{"view_html":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME","download_json":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME.json","view_paper":"https://pith.science/paper/SKR6DSJ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1218&json=true","fetch_graph":"https://pith.science/api/pith-number/SKR6DSJ75HZFDQGWFIPCOZNFME/graph.json","fetch_events":"https://pith.science/api/pith-number/SKR6DSJ75HZFDQGWFIPCOZNFME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME/action/storage_attestation","attest_author":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME/action/author_attestation","sign_citation":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME/action/citation_signature","submit_replication":"https://pith.science/pith/SKR6DSJ75HZFDQGWFIPCOZNFME/action/replication_record"}},"created_at":"2026-05-18T04:32:00.308110+00:00","updated_at":"2026-05-18T04:32:00.308110+00:00"}