{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7HGWKKHV2JV7FA54JBH3MKZZLU","short_pith_number":"pith:7HGWKKHV","schema_version":"1.0","canonical_sha256":"f9cd6528f5d26bf283bc484fb62b395d29abbb6c7218e29c8c91e3a32bb101a7","source":{"kind":"arxiv","id":"1101.1845","version":2},"attestation_state":"computed","paper":{"title":"Optimally Adapted Meshes for Finite Elements of Arbitrary Order and W1p Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Marie Mirebeau","submitted_at":"2011-01-10T15:22:05Z","abstract_excerpt":"Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W1p norm and we consider Lagrange finite elements of arbitrary polynomial order m-1. We establish sharp asymptotic error estimates as N tends to infinity when the optimal anisotropic triangulation is used. A similar problem has been studied earlier, but with the error measured in the Lp norm."},"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":"1101.1845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-10T15:22:05Z","cross_cats_sorted":[],"title_canon_sha256":"9dc75e4c705513efd359583b9835630a27ed4da597756b7d24bcce783d3ea45b","abstract_canon_sha256":"f42cd75c127f2d9217163c943a1110de6261eae3dfb4063977eae04911b22602"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:15.994889Z","signature_b64":"Eq/p/ctS2qJwP0cbLhruo8llxDQ5McxG5XamWaMTGfyB+GWOLE8DS+cePtIAvM/K6nFgyP1fQe+eziXT/DmsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9cd6528f5d26bf283bc484fb62b395d29abbb6c7218e29c8c91e3a32bb101a7","last_reissued_at":"2026-05-18T03:54:15.994239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:15.994239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimally Adapted Meshes for Finite Elements of Arbitrary Order and W1p Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Marie Mirebeau","submitted_at":"2011-01-10T15:22:05Z","abstract_excerpt":"Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all triangulations of at most N elements. The error is studied in the W1p norm and we consider Lagrange finite elements of arbitrary polynomial order m-1. We establish sharp asymptotic error estimates as N tends to infinity when the optimal anisotropic triangulation is used. A similar problem has been studied earlier, but with the error measured in the Lp norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1845","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":"1101.1845","created_at":"2026-05-18T03:54:15.994352+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1845v2","created_at":"2026-05-18T03:54:15.994352+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1845","created_at":"2026-05-18T03:54:15.994352+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HGWKKHV2JV7","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HGWKKHV2JV7FA54","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HGWKKHV","created_at":"2026-05-18T12:26:22.705136+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/7HGWKKHV2JV7FA54JBH3MKZZLU","json":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU.json","graph_json":"https://pith.science/api/pith-number/7HGWKKHV2JV7FA54JBH3MKZZLU/graph.json","events_json":"https://pith.science/api/pith-number/7HGWKKHV2JV7FA54JBH3MKZZLU/events.json","paper":"https://pith.science/paper/7HGWKKHV"},"agent_actions":{"view_html":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU","download_json":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU.json","view_paper":"https://pith.science/paper/7HGWKKHV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1845&json=true","fetch_graph":"https://pith.science/api/pith-number/7HGWKKHV2JV7FA54JBH3MKZZLU/graph.json","fetch_events":"https://pith.science/api/pith-number/7HGWKKHV2JV7FA54JBH3MKZZLU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU/action/storage_attestation","attest_author":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU/action/author_attestation","sign_citation":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU/action/citation_signature","submit_replication":"https://pith.science/pith/7HGWKKHV2JV7FA54JBH3MKZZLU/action/replication_record"}},"created_at":"2026-05-18T03:54:15.994352+00:00","updated_at":"2026-05-18T03:54:15.994352+00:00"}