{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QPVSL5MUUBSAFVB3U6NBLXFV3H","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ec5c77207517ca921d9f75bc342627c8735596b511bce6b7906e327f11efeee6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-22T07:24:50Z","title_canon_sha256":"137cb7baa9e1f5fbf7bb5f39eb99495d8af1b1f8a5a64c474f68176e9520d22d"},"schema_version":"1.0","source":{"id":"1408.5221","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5221","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5221v2","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5221","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"QPVSL5MUUBSA","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPVSL5MUUBSAFVB3","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPVSL5MU","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:558dfbf05ec45eb7e54c1f7ec9783b65dd9e45c0cbad64d87a397b4566441859","target":"graph","created_at":"2026-05-18T02:44:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples.","authors_text":"Mario Amrein, Thomas P. Wihler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-22T07:24:50Z","title":"Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5221","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7864567be9700fe078ea6d62b080e3494c854f555b5bf9504765259fea7713c8","target":"record","created_at":"2026-05-18T02:44:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ec5c77207517ca921d9f75bc342627c8735596b511bce6b7906e327f11efeee6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-08-22T07:24:50Z","title_canon_sha256":"137cb7baa9e1f5fbf7bb5f39eb99495d8af1b1f8a5a64c474f68176e9520d22d"},"schema_version":"1.0","source":{"id":"1408.5221","kind":"arxiv","version":2}},"canonical_sha256":"83eb25f594a06402d43ba79a15dcb5d9c85dcff92fa1c8b4bbdad1b5e2b601f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83eb25f594a06402d43ba79a15dcb5d9c85dcff92fa1c8b4bbdad1b5e2b601f4","first_computed_at":"2026-05-18T02:44:15.987778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:15.987778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rjwz0JqLAzcnKpM6kqc2SUgiMD1MNSJ36N7g8WwYinIakCAaoWbby6b0khC1xZcPx1IebQZZM14bH/lGalMQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:15.988297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5221","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7864567be9700fe078ea6d62b080e3494c854f555b5bf9504765259fea7713c8","sha256:558dfbf05ec45eb7e54c1f7ec9783b65dd9e45c0cbad64d87a397b4566441859"],"state_sha256":"0d6c90073c533e6d29863e995e59063ec8487d6feb794e9a4ec766f2d7f9603c"}