{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3I4PY73KUK62QW2R2JEHDK4IBA","short_pith_number":"pith:3I4PY73K","schema_version":"1.0","canonical_sha256":"da38fc7f6aa2bda85b51d24871ab8808139357f3638b064802fcc836b8e7e9c4","source":{"kind":"arxiv","id":"1711.04306","version":4},"attestation_state":"computed","paper":{"title":"The Virtual Element Method with curved edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. Russo, G. Vacca, L. Beir\\~ao da Veiga","submitted_at":"2017-11-12T15:08:11Z","abstract_excerpt":"In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \\geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence."},"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":"1711.04306","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T15:08:11Z","cross_cats_sorted":[],"title_canon_sha256":"456cdd8fd0fb80134c55ab4b6ba1cdf967e6207ed7e1604fbf8a74755361af51","abstract_canon_sha256":"25b1e8153ce54c477f899b75f6e16040cd67fafc84fb3cf1294efd6be23ae4c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:29.514433Z","signature_b64":"E7QSbpPb/2eEdiusoHFjr95RCLgMiDWB23nCmFd83wFvPjcUvCoyogU2IZNIgJ//+xbbi10KzKf+TpAm1DJRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da38fc7f6aa2bda85b51d24871ab8808139357f3638b064802fcc836b8e7e9c4","last_reissued_at":"2026-05-18T00:03:29.513876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:29.513876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Virtual Element Method with curved edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. Russo, G. Vacca, L. Beir\\~ao da Veiga","submitted_at":"2017-11-12T15:08:11Z","abstract_excerpt":"In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \\geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04306","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":"1711.04306","created_at":"2026-05-18T00:03:29.513965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.04306v4","created_at":"2026-05-18T00:03:29.513965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04306","created_at":"2026-05-18T00:03:29.513965+00:00"},{"alias_kind":"pith_short_12","alias_value":"3I4PY73KUK62","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3I4PY73KUK62QW2R","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3I4PY73K","created_at":"2026-05-18T12:30:58.224056+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/3I4PY73KUK62QW2R2JEHDK4IBA","json":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA.json","graph_json":"https://pith.science/api/pith-number/3I4PY73KUK62QW2R2JEHDK4IBA/graph.json","events_json":"https://pith.science/api/pith-number/3I4PY73KUK62QW2R2JEHDK4IBA/events.json","paper":"https://pith.science/paper/3I4PY73K"},"agent_actions":{"view_html":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA","download_json":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA.json","view_paper":"https://pith.science/paper/3I4PY73K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.04306&json=true","fetch_graph":"https://pith.science/api/pith-number/3I4PY73KUK62QW2R2JEHDK4IBA/graph.json","fetch_events":"https://pith.science/api/pith-number/3I4PY73KUK62QW2R2JEHDK4IBA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA/action/storage_attestation","attest_author":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA/action/author_attestation","sign_citation":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA/action/citation_signature","submit_replication":"https://pith.science/pith/3I4PY73KUK62QW2R2JEHDK4IBA/action/replication_record"}},"created_at":"2026-05-18T00:03:29.513965+00:00","updated_at":"2026-05-18T00:03:29.513965+00:00"}