{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ID3CPLCR46E3WVBJ6EQIY4BTYB","short_pith_number":"pith:ID3CPLCR","schema_version":"1.0","canonical_sha256":"40f627ac51e789bb5429f1208c7033c05f5508163d1b6f562a56a61f50166a2b","source":{"kind":"arxiv","id":"1106.6031","version":3},"attestation_state":"computed","paper":{"title":"A Study on Using Hierarchical Basis Error Estimates in Anisotropic Mesh Adaptation for the Finite Element Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lennard Kamenski","submitted_at":"2011-06-29T19:27:08Z","abstract_excerpt":"A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate metric which is often based on some type of Hessian recovery. Recently, the use of a global hierarchical basis error estimator was proposed for the development of an anisotropic metric tensor for the adaptive finite element solution. This study discusses the use of this method for a selection of different applications. Numerical results show that the method per"},"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":"1106.6031","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-06-29T19:27:08Z","cross_cats_sorted":[],"title_canon_sha256":"cd298e3e9a72dc886b1cb767e9e749ebe6bf023a145d7fae12abed9b1e24fbce","abstract_canon_sha256":"7ff7b8bb5181b12093e66c3e15fb8a74381c5240e88c36e81467e34bae2d8343"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:40.525166Z","signature_b64":"ObZ8bG0CVp8WMEXTsxVedyXKjWyVp1eOxUrmvNZEnm6KPmObB8ZNStyq4Zi+uZ4gQXYgfvfFN8hdoFYwp+HvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f627ac51e789bb5429f1208c7033c05f5508163d1b6f562a56a61f50166a2b","last_reissued_at":"2026-05-18T03:43:40.524412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:40.524412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Study on Using Hierarchical Basis Error Estimates in Anisotropic Mesh Adaptation for the Finite Element Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lennard Kamenski","submitted_at":"2011-06-29T19:27:08Z","abstract_excerpt":"A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate metric which is often based on some type of Hessian recovery. Recently, the use of a global hierarchical basis error estimator was proposed for the development of an anisotropic metric tensor for the adaptive finite element solution. This study discusses the use of this method for a selection of different applications. Numerical results show that the method per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.6031","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":"1106.6031","created_at":"2026-05-18T03:43:40.524548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.6031v3","created_at":"2026-05-18T03:43:40.524548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.6031","created_at":"2026-05-18T03:43:40.524548+00:00"},{"alias_kind":"pith_short_12","alias_value":"ID3CPLCR46E3","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"ID3CPLCR46E3WVBJ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"ID3CPLCR","created_at":"2026-05-18T12:26:30.835961+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/ID3CPLCR46E3WVBJ6EQIY4BTYB","json":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB.json","graph_json":"https://pith.science/api/pith-number/ID3CPLCR46E3WVBJ6EQIY4BTYB/graph.json","events_json":"https://pith.science/api/pith-number/ID3CPLCR46E3WVBJ6EQIY4BTYB/events.json","paper":"https://pith.science/paper/ID3CPLCR"},"agent_actions":{"view_html":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB","download_json":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB.json","view_paper":"https://pith.science/paper/ID3CPLCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.6031&json=true","fetch_graph":"https://pith.science/api/pith-number/ID3CPLCR46E3WVBJ6EQIY4BTYB/graph.json","fetch_events":"https://pith.science/api/pith-number/ID3CPLCR46E3WVBJ6EQIY4BTYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB/action/storage_attestation","attest_author":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB/action/author_attestation","sign_citation":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB/action/citation_signature","submit_replication":"https://pith.science/pith/ID3CPLCR46E3WVBJ6EQIY4BTYB/action/replication_record"}},"created_at":"2026-05-18T03:43:40.524548+00:00","updated_at":"2026-05-18T03:43:40.524548+00:00"}