{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7LKNR4WNH257VK53MHAZH2H2VM","short_pith_number":"pith:7LKNR4WN","schema_version":"1.0","canonical_sha256":"fad4d8f2cd3ebbfaabbb61c193e8faab08c8b088becfea0744dbd4e2610eb92c","source":{"kind":"arxiv","id":"1811.00825","version":1},"attestation_state":"computed","paper":{"title":"Primal dual mixed finite element methods for indefinite advection--diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Cuiyu He, Erik Burman","submitted_at":"2018-11-02T11:23:11Z","abstract_excerpt":"We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori error estimates in the energy- and the $L^2$-norms for the primal variable in the low Peclet regime. In the high Peclet regime we also prove optimal error estimates for the primal variable in the $H(div)$ norm for smooth solutions. Numerically we observe that the method eliminates the spurious oscillations close to interior layers that pollute the solution o"},"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":"1811.00825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-02T11:23:11Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"ded332937de3b7f5bf7aa0ed4070f1faafc5c2fb9cec33f02b705dd485b16d1b","abstract_canon_sha256":"033e8e6f6109c26ee338c2960a02e7ef313b4c262f3a73b8c34d91a383c7d7ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:39.138504Z","signature_b64":"Tp9oJYe1gSxv+slIHVq0ODO3rSCn8mjSqZEnuWJ+ep+HnlqCsBhLgCSR4uXwpMVLJkZTpVl+xdWdikTPsagsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fad4d8f2cd3ebbfaabbb61c193e8faab08c8b088becfea0744dbd4e2610eb92c","last_reissued_at":"2026-06-04T20:13:39.137993Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:39.137993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Primal dual mixed finite element methods for indefinite advection--diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Cuiyu He, Erik Burman","submitted_at":"2018-11-02T11:23:11Z","abstract_excerpt":"We consider primal-dual mixed finite element methods for the advection--diffusion equation. For the primal variable we use standard continuous finite element space and for the flux we use the Raviart-Thomas space. We prove optimal a priori error estimates in the energy- and the $L^2$-norms for the primal variable in the low Peclet regime. In the high Peclet regime we also prove optimal error estimates for the primal variable in the $H(div)$ norm for smooth solutions. Numerically we observe that the method eliminates the spurious oscillations close to interior layers that pollute the solution o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00825","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.00825/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":"1811.00825","created_at":"2026-06-04T20:13:39.138049+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00825v1","created_at":"2026-06-04T20:13:39.138049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00825","created_at":"2026-06-04T20:13:39.138049+00:00"},{"alias_kind":"pith_short_12","alias_value":"7LKNR4WNH257","created_at":"2026-06-04T20:13:39.138049+00:00"},{"alias_kind":"pith_short_16","alias_value":"7LKNR4WNH257VK53","created_at":"2026-06-04T20:13:39.138049+00:00"},{"alias_kind":"pith_short_8","alias_value":"7LKNR4WN","created_at":"2026-06-04T20:13:39.138049+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/7LKNR4WNH257VK53MHAZH2H2VM","json":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM.json","graph_json":"https://pith.science/api/pith-number/7LKNR4WNH257VK53MHAZH2H2VM/graph.json","events_json":"https://pith.science/api/pith-number/7LKNR4WNH257VK53MHAZH2H2VM/events.json","paper":"https://pith.science/paper/7LKNR4WN"},"agent_actions":{"view_html":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM","download_json":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM.json","view_paper":"https://pith.science/paper/7LKNR4WN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00825&json=true","fetch_graph":"https://pith.science/api/pith-number/7LKNR4WNH257VK53MHAZH2H2VM/graph.json","fetch_events":"https://pith.science/api/pith-number/7LKNR4WNH257VK53MHAZH2H2VM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM/action/storage_attestation","attest_author":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM/action/author_attestation","sign_citation":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM/action/citation_signature","submit_replication":"https://pith.science/pith/7LKNR4WNH257VK53MHAZH2H2VM/action/replication_record"}},"created_at":"2026-06-04T20:13:39.138049+00:00","updated_at":"2026-06-04T20:13:39.138049+00:00"}