{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DWPT635ADZ3BNVBQPMJ2CT763C","short_pith_number":"pith:DWPT635A","schema_version":"1.0","canonical_sha256":"1d9f3f6fa01e7616d4307b13a14ffed895b65ebfe9cdf5f40d92b480a91b1e60","source":{"kind":"arxiv","id":"1804.07898","version":2},"attestation_state":"computed","paper":{"title":"A posteriori error estimation and adaptivity in $hp$ virtual elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"G. Manzini, L. Beir\\~ao da Veiga, L. Mascotto","submitted_at":"2018-04-21T06:08:25Z","abstract_excerpt":"An explicit and computable error estimator for the $hp$ version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide $hp$ adaptive mesh refinements for very general polygonal meshes. In addition, a novel VEM $hp$ Cl\\'ement quasi-interpolant, instrumental for the a posteriori error analysis, is introduced. The performances of the adaptive method are validated by a number of numerical experiments."},"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":"1804.07898","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-21T06:08:25Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e9015a4cada1495aef99be438e7a69be203850f6221c77fa549d52854a96b263","abstract_canon_sha256":"82ef49034166f21ccaf9d324f2947bbe3deaad79862b57b525cd7c6e32284a16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:53.887397Z","signature_b64":"1fAld6ilpy1a55A6kitCIVBzc4hA47GDq0x48YouqQB3udouThGGW97Pus2Kv4Izj9jMQ1/dF8bkH+1Dxj7MCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d9f3f6fa01e7616d4307b13a14ffed895b65ebfe9cdf5f40d92b480a91b1e60","last_reissued_at":"2026-05-17T23:42:53.886780Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:53.886780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A posteriori error estimation and adaptivity in $hp$ virtual elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"G. Manzini, L. Beir\\~ao da Veiga, L. Mascotto","submitted_at":"2018-04-21T06:08:25Z","abstract_excerpt":"An explicit and computable error estimator for the $hp$ version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide $hp$ adaptive mesh refinements for very general polygonal meshes. In addition, a novel VEM $hp$ Cl\\'ement quasi-interpolant, instrumental for the a posteriori error analysis, is introduced. The performances of the adaptive method are validated by a number of numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07898","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":"1804.07898","created_at":"2026-05-17T23:42:53.886882+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.07898v2","created_at":"2026-05-17T23:42:53.886882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07898","created_at":"2026-05-17T23:42:53.886882+00:00"},{"alias_kind":"pith_short_12","alias_value":"DWPT635ADZ3B","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DWPT635ADZ3BNVBQ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DWPT635A","created_at":"2026-05-18T12:32:19.392346+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/DWPT635ADZ3BNVBQPMJ2CT763C","json":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C.json","graph_json":"https://pith.science/api/pith-number/DWPT635ADZ3BNVBQPMJ2CT763C/graph.json","events_json":"https://pith.science/api/pith-number/DWPT635ADZ3BNVBQPMJ2CT763C/events.json","paper":"https://pith.science/paper/DWPT635A"},"agent_actions":{"view_html":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C","download_json":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C.json","view_paper":"https://pith.science/paper/DWPT635A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.07898&json=true","fetch_graph":"https://pith.science/api/pith-number/DWPT635ADZ3BNVBQPMJ2CT763C/graph.json","fetch_events":"https://pith.science/api/pith-number/DWPT635ADZ3BNVBQPMJ2CT763C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C/action/storage_attestation","attest_author":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C/action/author_attestation","sign_citation":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C/action/citation_signature","submit_replication":"https://pith.science/pith/DWPT635ADZ3BNVBQPMJ2CT763C/action/replication_record"}},"created_at":"2026-05-17T23:42:53.886882+00:00","updated_at":"2026-05-17T23:42:53.886882+00:00"}