{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:F3BTTL5F27SZQ4GTHNVABMESEP","short_pith_number":"pith:F3BTTL5F","schema_version":"1.0","canonical_sha256":"2ec339afa5d7e59870d33b6a00b09223e6f67c1f9430886af08d4917f30c7564","source":{"kind":"arxiv","id":"1804.03998","version":2},"attestation_state":"computed","paper":{"title":"Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Dan Li, Junping Wang","submitted_at":"2018-04-11T14:12:20Z","abstract_excerpt":"This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by the weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of ${\\cal O}(h^r)$, $1.5\\leq r \\leq 2$, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is ${\\cal O}(h)$ for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finit"},"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":"1804.03998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T14:12:20Z","cross_cats_sorted":[],"title_canon_sha256":"6f73e67af8c51dc4be9ac25770658018a27be0207e3ca6a341d7a8b7a1df5d09","abstract_canon_sha256":"11ceac61f918457140b25d50dc1e1a28c634bac5cbf84b52b2cf3ce721ac9aee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:48.144101Z","signature_b64":"lUhxm/OW6YHNL2DlOGhgb20v5qzNn9fQqUQymk5lSHyXK2YnMrb3dhlAGjg33IMv6KxvTEnLNiquMoJ84X97BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ec339afa5d7e59870d33b6a00b09223e6f67c1f9430886af08d4917f30c7564","last_reissued_at":"2026-05-18T00:12:48.143483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:48.143483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Chunmei Wang, Dan Li, Junping Wang","submitted_at":"2018-04-11T14:12:20Z","abstract_excerpt":"This article presents a superconvergence for the gradient approximation of the second order elliptic equation discretized by the weak Galerkin finite element methods on nonuniform rectangular partitions. The result shows a convergence of ${\\cal O}(h^r)$, $1.5\\leq r \\leq 2$, for the numerical gradient obtained from the lowest order weak Galerkin element consisting of piecewise linear and constant functions. For this numerical scheme, the optimal order of error estimate is ${\\cal O}(h)$ for the gradient approximation. The superconvergence reveals a superior performance of the weak Galerkin finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03998","kind":"arxiv","version":2},"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":"1804.03998","created_at":"2026-05-18T00:12:48.143599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03998v2","created_at":"2026-05-18T00:12:48.143599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03998","created_at":"2026-05-18T00:12:48.143599+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3BTTL5F27SZ","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3BTTL5F27SZQ4GT","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3BTTL5F","created_at":"2026-05-18T12:32:22.470017+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/F3BTTL5F27SZQ4GTHNVABMESEP","json":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP.json","graph_json":"https://pith.science/api/pith-number/F3BTTL5F27SZQ4GTHNVABMESEP/graph.json","events_json":"https://pith.science/api/pith-number/F3BTTL5F27SZQ4GTHNVABMESEP/events.json","paper":"https://pith.science/paper/F3BTTL5F"},"agent_actions":{"view_html":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP","download_json":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP.json","view_paper":"https://pith.science/paper/F3BTTL5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03998&json=true","fetch_graph":"https://pith.science/api/pith-number/F3BTTL5F27SZQ4GTHNVABMESEP/graph.json","fetch_events":"https://pith.science/api/pith-number/F3BTTL5F27SZQ4GTHNVABMESEP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP/action/storage_attestation","attest_author":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP/action/author_attestation","sign_citation":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP/action/citation_signature","submit_replication":"https://pith.science/pith/F3BTTL5F27SZQ4GTHNVABMESEP/action/replication_record"}},"created_at":"2026-05-18T00:12:48.143599+00:00","updated_at":"2026-05-18T00:12:48.143599+00:00"}