{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:RVCQLSV7QKHZKOEV7AIO5M6NRV","short_pith_number":"pith:RVCQLSV7","schema_version":"1.0","canonical_sha256":"8d4505cabf828f953895f810eeb3cd8d49635adb5b23f93ac69b387871c719f1","source":{"kind":"arxiv","id":"1006.0191","version":2},"attestation_state":"computed","paper":{"title":"Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lennard Kamenski, Weizhang Huang, Xianping Li","submitted_at":"2010-06-01T17:30:49Z","abstract_excerpt":"Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error estimator for the development of an anisotropic metric tensor needed for the adaptive finite element solution of variational problems. The new metric tensor is completely a~posteriori and based on residual, edge jumps and the hierarchical basis error estimator. Numerical results show that it performs comparable with existing metric tensors based on Hessian "},"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":"1006.0191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-06-01T17:30:49Z","cross_cats_sorted":[],"title_canon_sha256":"2f0302c4c0235240a830fb3e39342d43b7c62de2e3c87f2ddc78d9d2d0dec69b","abstract_canon_sha256":"ebb23844237a1a391e58b0c96c1212c121177625ea8595fb7333b823780c9e3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:48.529642Z","signature_b64":"s3aSyeNxmRPg4P25DWT5ZXj8UpNvpKcvPtZF6zxhRaeySNbkL5csn3NImXwFqR0IqBOiv8Og+u/ujZZkBG/oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d4505cabf828f953895f810eeb3cd8d49635adb5b23f93ac69b387871c719f1","last_reissued_at":"2026-05-18T02:23:48.529049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:48.529049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lennard Kamenski, Weizhang Huang, Xianping Li","submitted_at":"2010-06-01T17:30:49Z","abstract_excerpt":"Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error estimator for the development of an anisotropic metric tensor needed for the adaptive finite element solution of variational problems. The new metric tensor is completely a~posteriori and based on residual, edge jumps and the hierarchical basis error estimator. Numerical results show that it performs comparable with existing metric tensors based on Hessian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0191","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":"1006.0191","created_at":"2026-05-18T02:23:48.529130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.0191v2","created_at":"2026-05-18T02:23:48.529130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0191","created_at":"2026-05-18T02:23:48.529130+00:00"},{"alias_kind":"pith_short_12","alias_value":"RVCQLSV7QKHZ","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"RVCQLSV7QKHZKOEV","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"RVCQLSV7","created_at":"2026-05-18T12:26:13.927090+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/RVCQLSV7QKHZKOEV7AIO5M6NRV","json":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV.json","graph_json":"https://pith.science/api/pith-number/RVCQLSV7QKHZKOEV7AIO5M6NRV/graph.json","events_json":"https://pith.science/api/pith-number/RVCQLSV7QKHZKOEV7AIO5M6NRV/events.json","paper":"https://pith.science/paper/RVCQLSV7"},"agent_actions":{"view_html":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV","download_json":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV.json","view_paper":"https://pith.science/paper/RVCQLSV7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.0191&json=true","fetch_graph":"https://pith.science/api/pith-number/RVCQLSV7QKHZKOEV7AIO5M6NRV/graph.json","fetch_events":"https://pith.science/api/pith-number/RVCQLSV7QKHZKOEV7AIO5M6NRV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV/action/storage_attestation","attest_author":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV/action/author_attestation","sign_citation":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV/action/citation_signature","submit_replication":"https://pith.science/pith/RVCQLSV7QKHZKOEV7AIO5M6NRV/action/replication_record"}},"created_at":"2026-05-18T02:23:48.529130+00:00","updated_at":"2026-05-18T02:23:48.529130+00:00"}