{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AE3EKJAOD4PVDEU3IPIKW6UYH5","short_pith_number":"pith:AE3EKJAO","schema_version":"1.0","canonical_sha256":"013645240e1f1f51929b43d0ab7a983f60cf3b9ca9194779ac2cad8a29ca9da8","source":{"kind":"arxiv","id":"1710.09913","version":5},"attestation_state":"computed","paper":{"title":"Double-grid quadrature with interpolation-projection (DoGIP) as a novel discretisation approach: An application to FEM on simplexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jaroslav Vond\\v{r}ejc","submitted_at":"2017-10-26T21:14:25Z","abstract_excerpt":"This paper is focused on the double-grid integration with interpolation-projection (DoGIP), which is a novel matrix-free discretisation method of variational formulations introduced for Fourier--Galerkin approximation. Here, it is described as a more general approach with an application to the finite element method (FEM) on simplexes. The approach is based on treating the trial and a test function in variational formulation together, which leads to the decomposition of a linear system into interpolation and (block) diagonal matrices. It usually leads to reduced memory demands, especially for h"},"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":"1710.09913","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-26T21:14:25Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1f45ecbc470d0688430628e749b62d40697e94ad318c7a19170448935054421a","abstract_canon_sha256":"eadf00ce0de571b2fa87dd49be0c6f06fc13344f92c019349afa2b94e1dae34b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:07.807514Z","signature_b64":"tfazHHPnHr8ggSENwU+jO3nR2a9G73UgLcljmEZIe9KqEwwdzeUwHS8zPpSC4YtzTVi6SyYHxGjI9nNKuV4aAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"013645240e1f1f51929b43d0ab7a983f60cf3b9ca9194779ac2cad8a29ca9da8","last_reissued_at":"2026-06-04T19:11:07.806998Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:07.806998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double-grid quadrature with interpolation-projection (DoGIP) as a novel discretisation approach: An application to FEM on simplexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Jaroslav Vond\\v{r}ejc","submitted_at":"2017-10-26T21:14:25Z","abstract_excerpt":"This paper is focused on the double-grid integration with interpolation-projection (DoGIP), which is a novel matrix-free discretisation method of variational formulations introduced for Fourier--Galerkin approximation. Here, it is described as a more general approach with an application to the finite element method (FEM) on simplexes. The approach is based on treating the trial and a test function in variational formulation together, which leads to the decomposition of a linear system into interpolation and (block) diagonal matrices. It usually leads to reduced memory demands, especially for h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09913","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.09913/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1710.09913","created_at":"2026-06-04T19:11:07.807072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09913v5","created_at":"2026-06-04T19:11:07.807072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09913","created_at":"2026-06-04T19:11:07.807072+00:00"},{"alias_kind":"pith_short_12","alias_value":"AE3EKJAOD4PV","created_at":"2026-06-04T19:11:07.807072+00:00"},{"alias_kind":"pith_short_16","alias_value":"AE3EKJAOD4PVDEU3","created_at":"2026-06-04T19:11:07.807072+00:00"},{"alias_kind":"pith_short_8","alias_value":"AE3EKJAO","created_at":"2026-06-04T19:11:07.807072+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/AE3EKJAOD4PVDEU3IPIKW6UYH5","json":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5.json","graph_json":"https://pith.science/api/pith-number/AE3EKJAOD4PVDEU3IPIKW6UYH5/graph.json","events_json":"https://pith.science/api/pith-number/AE3EKJAOD4PVDEU3IPIKW6UYH5/events.json","paper":"https://pith.science/paper/AE3EKJAO"},"agent_actions":{"view_html":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5","download_json":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5.json","view_paper":"https://pith.science/paper/AE3EKJAO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09913&json=true","fetch_graph":"https://pith.science/api/pith-number/AE3EKJAOD4PVDEU3IPIKW6UYH5/graph.json","fetch_events":"https://pith.science/api/pith-number/AE3EKJAOD4PVDEU3IPIKW6UYH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5/action/storage_attestation","attest_author":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5/action/author_attestation","sign_citation":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5/action/citation_signature","submit_replication":"https://pith.science/pith/AE3EKJAOD4PVDEU3IPIKW6UYH5/action/replication_record"}},"created_at":"2026-06-04T19:11:07.807072+00:00","updated_at":"2026-06-04T19:11:07.807072+00:00"}