{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CADO53KRBOU4OGY5PRQY4MLNFU","short_pith_number":"pith:CADO53KR","schema_version":"1.0","canonical_sha256":"1006eeed510ba9c71b1d7c618e316d2d2d4af704561bc40c08ea993451f9fd30","source":{"kind":"arxiv","id":"1107.2143","version":1},"attestation_state":"computed","paper":{"title":"Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear Poisson-Boltzmann Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael Holst, Ryan Szypowski, Yunrong Zhu","submitted_at":"2011-07-11T20:49:07Z","abstract_excerpt":"In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such as the nonlinear Poisson-Boltzmann equation and its regularizations. The algorithm we study consists of the standard SOLVE-ESTIMATE-MARK-REFINE procedure common to many adaptive finite element algorithms, but where the SOLVE step involves only a full solve on the coarsest level, and the remaining levels involve only single Newton updates to the previous app"},"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":"1107.2143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-07-11T20:49:07Z","cross_cats_sorted":[],"title_canon_sha256":"f88c5eb17de0aedeb7639d7022ebe45f860ad8fbaca1f7359894fee60d3bbd06","abstract_canon_sha256":"89b435a2d4a6826610e4f13de509c2f0233592d1d751f977fd1194662ebd2284"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:21.732029Z","signature_b64":"O/grzVn9GfHprgy2201OjMf9k5ITE3yoIoKdZiaPBqmaXKI1h+ApfVTxpbyTs2PtFvaEcuGaFZXVKZ2R4eTLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1006eeed510ba9c71b1d7c618e316d2d2d4af704561bc40c08ea993451f9fd30","last_reissued_at":"2026-05-18T01:08:21.731354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:21.731354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear Poisson-Boltzmann Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Michael Holst, Ryan Szypowski, Yunrong Zhu","submitted_at":"2011-07-11T20:49:07Z","abstract_excerpt":"In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such as the nonlinear Poisson-Boltzmann equation and its regularizations. The algorithm we study consists of the standard SOLVE-ESTIMATE-MARK-REFINE procedure common to many adaptive finite element algorithms, but where the SOLVE step involves only a full solve on the coarsest level, and the remaining levels involve only single Newton updates to the previous app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2143","kind":"arxiv","version":1},"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":"1107.2143","created_at":"2026-05-18T01:08:21.731457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.2143v1","created_at":"2026-05-18T01:08:21.731457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2143","created_at":"2026-05-18T01:08:21.731457+00:00"},{"alias_kind":"pith_short_12","alias_value":"CADO53KRBOU4","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CADO53KRBOU4OGY5","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CADO53KR","created_at":"2026-05-18T12:26:26.731475+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/CADO53KRBOU4OGY5PRQY4MLNFU","json":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU.json","graph_json":"https://pith.science/api/pith-number/CADO53KRBOU4OGY5PRQY4MLNFU/graph.json","events_json":"https://pith.science/api/pith-number/CADO53KRBOU4OGY5PRQY4MLNFU/events.json","paper":"https://pith.science/paper/CADO53KR"},"agent_actions":{"view_html":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU","download_json":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU.json","view_paper":"https://pith.science/paper/CADO53KR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.2143&json=true","fetch_graph":"https://pith.science/api/pith-number/CADO53KRBOU4OGY5PRQY4MLNFU/graph.json","fetch_events":"https://pith.science/api/pith-number/CADO53KRBOU4OGY5PRQY4MLNFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU/action/storage_attestation","attest_author":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU/action/author_attestation","sign_citation":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU/action/citation_signature","submit_replication":"https://pith.science/pith/CADO53KRBOU4OGY5PRQY4MLNFU/action/replication_record"}},"created_at":"2026-05-18T01:08:21.731457+00:00","updated_at":"2026-05-18T01:08:21.731457+00:00"}