{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3I4PY73KUK62QW2R2JEHDK4IBA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"25b1e8153ce54c477f899b75f6e16040cd67fafc84fb3cf1294efd6be23ae4c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T15:08:11Z","title_canon_sha256":"456cdd8fd0fb80134c55ab4b6ba1cdf967e6207ed7e1604fbf8a74755361af51"},"schema_version":"1.0","source":{"id":"1711.04306","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04306","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04306v4","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04306","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"3I4PY73KUK62","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3I4PY73KUK62QW2R","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3I4PY73K","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:ed786650dfe112d6be88e8d9f6388379874fa0f252864e7deb11bf5dc5c6d5b6","target":"graph","created_at":"2026-05-18T00:03:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"A. Russo, G. Vacca, L. Beir\\~ao da Veiga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T15:08:11Z","title":"The Virtual Element Method with curved edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04306","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:738cc34df4a08ad478f33c0f91e92ed7b531db70df5258cfc29b97c9ed4c0b16","target":"record","created_at":"2026-05-18T00:03:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"25b1e8153ce54c477f899b75f6e16040cd67fafc84fb3cf1294efd6be23ae4c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-11-12T15:08:11Z","title_canon_sha256":"456cdd8fd0fb80134c55ab4b6ba1cdf967e6207ed7e1604fbf8a74755361af51"},"schema_version":"1.0","source":{"id":"1711.04306","kind":"arxiv","version":4}},"canonical_sha256":"da38fc7f6aa2bda85b51d24871ab8808139357f3638b064802fcc836b8e7e9c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da38fc7f6aa2bda85b51d24871ab8808139357f3638b064802fcc836b8e7e9c4","first_computed_at":"2026-05-18T00:03:29.513876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:29.513876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E7QSbpPb/2eEdiusoHFjr95RCLgMiDWB23nCmFd83wFvPjcUvCoyogU2IZNIgJ//+xbbi10KzKf+TpAm1DJRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:29.514433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04306","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:738cc34df4a08ad478f33c0f91e92ed7b531db70df5258cfc29b97c9ed4c0b16","sha256:ed786650dfe112d6be88e8d9f6388379874fa0f252864e7deb11bf5dc5c6d5b6"],"state_sha256":"a586b56de8c4bc3391e30de20ac3d61dfcc018ad9bcf79b068fa3a46b93217da"}