{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GASRHFRLVAF43TJT4IBPCDJGN7","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":"a430b728612cfebf9275725be080463f228e02dc5270b873e92b33d02fb2618e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-22T16:46:20Z","title_canon_sha256":"2291ab8a5c1b5582ee849294af67fc271085cbaa9eb84f66a0cdd7e9f0d824ec"},"schema_version":"1.0","source":{"id":"2402.14691","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.14691","created_at":"2026-07-05T07:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"2402.14691v2","created_at":"2026-07-05T07:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.14691","created_at":"2026-07-05T07:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"GASRHFRLVAF4","created_at":"2026-07-05T07:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"GASRHFRLVAF43TJT","created_at":"2026-07-05T07:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"GASRHFRL","created_at":"2026-07-05T07:48:35Z"}],"graph_snapshots":[{"event_id":"sha256:d3332bae78bfc51c9293f89d41ed172e21102a144370acf478e7f46a80942d59","target":"graph","created_at":"2026-07-05T07:48:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.14691/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A new moving mesh scheme based on the Lagrange-Galerkin method for the approximation of the one-dimensional convection-diffusion equation is studied. The mesh movement, which is prescribed by a discretized dynamical system for the nodal points, follows the direction of convection. It is shown that under a restriction of the time increment the mesh movement cannot lead to an overlap of the elements and therefore an invalid mesh. For the linear element, optimal error estimates in the $\\ell^\\infty(L^2) \\cap \\ell^2(H_0^1)$ norm are proved in case of both, a first-order backward Euler method and a ","authors_text":"Hirofumi Notsu, Kharisma Surya Putri, Niklas Kolbe, Tatsuki Mizuochi","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-22T16:46:20Z","title":"Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.14691","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":"sha256:1bdef0e7b970601380ec765f9e6e541374873f612bd61c35338ca5419d876f20","target":"record","created_at":"2026-07-05T07:48:35Z","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":"a430b728612cfebf9275725be080463f228e02dc5270b873e92b33d02fb2618e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-22T16:46:20Z","title_canon_sha256":"2291ab8a5c1b5582ee849294af67fc271085cbaa9eb84f66a0cdd7e9f0d824ec"},"schema_version":"1.0","source":{"id":"2402.14691","kind":"arxiv","version":2}},"canonical_sha256":"302513962ba80bcdcd33e202f10d266fdc6469b3eb740df761827e5e17a9cd99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"302513962ba80bcdcd33e202f10d266fdc6469b3eb740df761827e5e17a9cd99","first_computed_at":"2026-07-05T07:48:35.447870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:48:35.447870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yyY/CRv7AjpLcLflW0AC8gCR4MupxL/P1gXzSP5GuskX1UxO197zP41ZHwsPMevPs48IokuWwAcITqki26SbCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:48:35.448263Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.14691","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bdef0e7b970601380ec765f9e6e541374873f612bd61c35338ca5419d876f20","sha256:d3332bae78bfc51c9293f89d41ed172e21102a144370acf478e7f46a80942d59"],"state_sha256":"2d802e9206ef22da1d715ce6f92ebd4907ce1f07f865a4a9f21eeb2ca38d1808"}