{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GASRHFRLVAF43TJT4IBPCDJGN7","short_pith_number":"pith:GASRHFRL","schema_version":"1.0","canonical_sha256":"302513962ba80bcdcd33e202f10d266fdc6469b3eb740df761827e5e17a9cd99","source":{"kind":"arxiv","id":"2402.14691","version":2},"attestation_state":"computed","paper":{"title":"Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hirofumi Notsu, Kharisma Surya Putri, Niklas Kolbe, Tatsuki Mizuochi","submitted_at":"2024-02-22T16:46:20Z","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 "},"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":"2402.14691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-22T16:46:20Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2291ab8a5c1b5582ee849294af67fc271085cbaa9eb84f66a0cdd7e9f0d824ec","abstract_canon_sha256":"a430b728612cfebf9275725be080463f228e02dc5270b873e92b33d02fb2618e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:48:35.448263Z","signature_b64":"yyY/CRv7AjpLcLflW0AC8gCR4MupxL/P1gXzSP5GuskX1UxO197zP41ZHwsPMevPs48IokuWwAcITqki26SbCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"302513962ba80bcdcd33e202f10d266fdc6469b3eb740df761827e5e17a9cd99","last_reissued_at":"2026-07-05T07:48:35.447870Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:48:35.447870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Error Estimates for First- and Second-Order Lagrange-Galerkin Moving Mesh Schemes for the One-Dimensional Convection-Diffusion Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hirofumi Notsu, Kharisma Surya Putri, Niklas Kolbe, Tatsuki Mizuochi","submitted_at":"2024-02-22T16:46:20Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.14691","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.14691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2402.14691","created_at":"2026-07-05T07:48:35.447920+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.14691v2","created_at":"2026-07-05T07:48:35.447920+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.14691","created_at":"2026-07-05T07:48:35.447920+00:00"},{"alias_kind":"pith_short_12","alias_value":"GASRHFRLVAF4","created_at":"2026-07-05T07:48:35.447920+00:00"},{"alias_kind":"pith_short_16","alias_value":"GASRHFRLVAF43TJT","created_at":"2026-07-05T07:48:35.447920+00:00"},{"alias_kind":"pith_short_8","alias_value":"GASRHFRL","created_at":"2026-07-05T07:48:35.447920+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/GASRHFRLVAF43TJT4IBPCDJGN7","json":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7.json","graph_json":"https://pith.science/api/pith-number/GASRHFRLVAF43TJT4IBPCDJGN7/graph.json","events_json":"https://pith.science/api/pith-number/GASRHFRLVAF43TJT4IBPCDJGN7/events.json","paper":"https://pith.science/paper/GASRHFRL"},"agent_actions":{"view_html":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7","download_json":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7.json","view_paper":"https://pith.science/paper/GASRHFRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.14691&json=true","fetch_graph":"https://pith.science/api/pith-number/GASRHFRLVAF43TJT4IBPCDJGN7/graph.json","fetch_events":"https://pith.science/api/pith-number/GASRHFRLVAF43TJT4IBPCDJGN7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7/action/storage_attestation","attest_author":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7/action/author_attestation","sign_citation":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7/action/citation_signature","submit_replication":"https://pith.science/pith/GASRHFRLVAF43TJT4IBPCDJGN7/action/replication_record"}},"created_at":"2026-07-05T07:48:35.447920+00:00","updated_at":"2026-07-05T07:48:35.447920+00:00"}