{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JUJF3TAYGT2Q434YNDUN4MSZXC","short_pith_number":"pith:JUJF3TAY","schema_version":"1.0","canonical_sha256":"4d125dcc1834f50e6f9868e8de3259b8be9b66f90f69dc010d151e3fc9e757e8","source":{"kind":"arxiv","id":"1704.08046","version":3},"attestation_state":"computed","paper":{"title":"On the exponent of exponential convergence of the $p$-version FEM spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Zhaonan Dong","submitted_at":"2017-04-26T10:26:23Z","abstract_excerpt":"We study the exponent of the exponential rate of convergence in terms of the number of degrees of freedom for various non-standard {$p$-version} finite element spaces employing reduced cardinality basis. More specifically, we show that serendipity finite element methods and discontinuous Galerkin finite element methods with total degree $\\mathcal{P}_p$ basis have a faster exponential convergence with respect to the number of degrees of freedom than their counterparts employing the tensor product $\\mathcal{Q}_p$ basis for quadrilateral/hexahedral elements, for piecewise analytic problems under "},"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":"1704.08046","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-26T10:26:23Z","cross_cats_sorted":[],"title_canon_sha256":"50c2aaa0dbaedb4916bc4319e0a5ffde732f390223998f35db3a880c7120b244","abstract_canon_sha256":"30483a3236e500ae48ba9a9cb33185ebf60a34099a2dcfff113b0b00305f3a21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:49.724270Z","signature_b64":"nh92ULZrsMK3ElK82HrTv4z1i8wf7PCfn/nS0NR/X5f9GsLIHEQcCA+k7CkyCQR3VYp37gQbVeSJEtViq+VlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d125dcc1834f50e6f9868e8de3259b8be9b66f90f69dc010d151e3fc9e757e8","last_reissued_at":"2026-05-17T23:51:49.723520Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:49.723520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the exponent of exponential convergence of the $p$-version FEM spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Zhaonan Dong","submitted_at":"2017-04-26T10:26:23Z","abstract_excerpt":"We study the exponent of the exponential rate of convergence in terms of the number of degrees of freedom for various non-standard {$p$-version} finite element spaces employing reduced cardinality basis. More specifically, we show that serendipity finite element methods and discontinuous Galerkin finite element methods with total degree $\\mathcal{P}_p$ basis have a faster exponential convergence with respect to the number of degrees of freedom than their counterparts employing the tensor product $\\mathcal{Q}_p$ basis for quadrilateral/hexahedral elements, for piecewise analytic problems under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08046","kind":"arxiv","version":3},"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":"1704.08046","created_at":"2026-05-17T23:51:49.723652+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.08046v3","created_at":"2026-05-17T23:51:49.723652+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08046","created_at":"2026-05-17T23:51:49.723652+00:00"},{"alias_kind":"pith_short_12","alias_value":"JUJF3TAYGT2Q","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JUJF3TAYGT2Q434Y","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JUJF3TAY","created_at":"2026-05-18T12:31:24.725408+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/JUJF3TAYGT2Q434YNDUN4MSZXC","json":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC.json","graph_json":"https://pith.science/api/pith-number/JUJF3TAYGT2Q434YNDUN4MSZXC/graph.json","events_json":"https://pith.science/api/pith-number/JUJF3TAYGT2Q434YNDUN4MSZXC/events.json","paper":"https://pith.science/paper/JUJF3TAY"},"agent_actions":{"view_html":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC","download_json":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC.json","view_paper":"https://pith.science/paper/JUJF3TAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.08046&json=true","fetch_graph":"https://pith.science/api/pith-number/JUJF3TAYGT2Q434YNDUN4MSZXC/graph.json","fetch_events":"https://pith.science/api/pith-number/JUJF3TAYGT2Q434YNDUN4MSZXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC/action/storage_attestation","attest_author":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC/action/author_attestation","sign_citation":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC/action/citation_signature","submit_replication":"https://pith.science/pith/JUJF3TAYGT2Q434YNDUN4MSZXC/action/replication_record"}},"created_at":"2026-05-17T23:51:49.723652+00:00","updated_at":"2026-05-17T23:51:49.723652+00:00"}