{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:I44OBWVXKF73LYZSZXDDIGHSKU","short_pith_number":"pith:I44OBWVX","schema_version":"1.0","canonical_sha256":"4738e0dab7517fb5e332cdc63418f2553300a36e56d21ba265b2d3e17edc9839","source":{"kind":"arxiv","id":"2307.00822","version":3},"attestation_state":"computed","paper":{"title":"Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Anupam Sharma, Baskar Ganapathysubramanian, Biswajit Khara, Kumar Saurabh, Robert Dyja","submitted_at":"2023-07-03T08:01:56Z","abstract_excerpt":"We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with"},"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":"2307.00822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-07-03T08:01:56Z","cross_cats_sorted":["cs.NA","math.AP"],"title_canon_sha256":"d2792a0bdb763bffa1b2da67504d243dfb97702f4c0c38a5e70511935e73d182","abstract_canon_sha256":"dd3d87c79c4ff3e26b96c25d62b486ac110736b42ac03678dcb01c09212b9934"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:03.519414Z","signature_b64":"ifwyHarnI5e6RoD3g2/lSnbeSMvMIF/hCODEmc4lbgQUpOWqG7zZhuFn7Lt7Rn0B5Eq9PZliHktp+FOFGSEhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4738e0dab7517fb5e332cdc63418f2553300a36e56d21ba265b2d3e17edc9839","last_reissued_at":"2026-07-05T09:39:03.518943Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:03.518943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Anupam Sharma, Baskar Ganapathysubramanian, Biswajit Khara, Kumar Saurabh, Robert Dyja","submitted_at":"2023-07-03T08:01:56Z","abstract_excerpt":"We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.00822","kind":"arxiv","version":3},"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/2307.00822/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":"2307.00822","created_at":"2026-07-05T09:39:03.519014+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.00822v3","created_at":"2026-07-05T09:39:03.519014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.00822","created_at":"2026-07-05T09:39:03.519014+00:00"},{"alias_kind":"pith_short_12","alias_value":"I44OBWVXKF73","created_at":"2026-07-05T09:39:03.519014+00:00"},{"alias_kind":"pith_short_16","alias_value":"I44OBWVXKF73LYZS","created_at":"2026-07-05T09:39:03.519014+00:00"},{"alias_kind":"pith_short_8","alias_value":"I44OBWVX","created_at":"2026-07-05T09:39:03.519014+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/I44OBWVXKF73LYZSZXDDIGHSKU","json":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU.json","graph_json":"https://pith.science/api/pith-number/I44OBWVXKF73LYZSZXDDIGHSKU/graph.json","events_json":"https://pith.science/api/pith-number/I44OBWVXKF73LYZSZXDDIGHSKU/events.json","paper":"https://pith.science/paper/I44OBWVX"},"agent_actions":{"view_html":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU","download_json":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU.json","view_paper":"https://pith.science/paper/I44OBWVX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.00822&json=true","fetch_graph":"https://pith.science/api/pith-number/I44OBWVXKF73LYZSZXDDIGHSKU/graph.json","fetch_events":"https://pith.science/api/pith-number/I44OBWVXKF73LYZSZXDDIGHSKU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU/action/storage_attestation","attest_author":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU/action/author_attestation","sign_citation":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU/action/citation_signature","submit_replication":"https://pith.science/pith/I44OBWVXKF73LYZSZXDDIGHSKU/action/replication_record"}},"created_at":"2026-07-05T09:39:03.519014+00:00","updated_at":"2026-07-05T09:39:03.519014+00:00"}