{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LDMAQNLZ2KIOKGXU7SXOF4HDNA","short_pith_number":"pith:LDMAQNLZ","schema_version":"1.0","canonical_sha256":"58d8083579d290e51af4fcaee2f0e3680deb052d35c7d06b2a938cd6aead4d52","source":{"kind":"arxiv","id":"2506.03751","version":1},"attestation_state":"computed","paper":{"title":"Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ankit Kumar, Sangita Yadav, Sarvesh Kumar","submitted_at":"2025-06-04T09:18:35Z","abstract_excerpt":"We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and L2-norm. Several numerical experiments are conducted to validate the theoretical findings and as"},"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":"2506.03751","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2025-06-04T09:18:35Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"88226aee49afb82cc39fbebab3be3d487382b4a59051d32d13c57d51d5961ec4","abstract_canon_sha256":"ab5cc8ee7e3cb311781bedd6ed7ccaf31e485dbfd9f99fb3a3e096c6763bbff6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:51.400967Z","signature_b64":"/8fyhgALJpIiB5N1zeammkXTRWICQ7602zJWUZbd5qi5KrZodqIS+RxdoSvkhchsdgNHzRcv1dtjtWBlBVuvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d8083579d290e51af4fcaee2f0e3680deb052d35c7d06b2a938cd6aead4d52","last_reissued_at":"2026-07-05T11:15:51.400502Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:51.400502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ankit Kumar, Sangita Yadav, Sarvesh Kumar","submitted_at":"2025-06-04T09:18:35Z","abstract_excerpt":"We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and L2-norm. Several numerical experiments are conducted to validate the theoretical findings and as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03751","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/2506.03751/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":"2506.03751","created_at":"2026-07-05T11:15:51.400559+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.03751v1","created_at":"2026-07-05T11:15:51.400559+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03751","created_at":"2026-07-05T11:15:51.400559+00:00"},{"alias_kind":"pith_short_12","alias_value":"LDMAQNLZ2KIO","created_at":"2026-07-05T11:15:51.400559+00:00"},{"alias_kind":"pith_short_16","alias_value":"LDMAQNLZ2KIOKGXU","created_at":"2026-07-05T11:15:51.400559+00:00"},{"alias_kind":"pith_short_8","alias_value":"LDMAQNLZ","created_at":"2026-07-05T11:15:51.400559+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/LDMAQNLZ2KIOKGXU7SXOF4HDNA","json":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA.json","graph_json":"https://pith.science/api/pith-number/LDMAQNLZ2KIOKGXU7SXOF4HDNA/graph.json","events_json":"https://pith.science/api/pith-number/LDMAQNLZ2KIOKGXU7SXOF4HDNA/events.json","paper":"https://pith.science/paper/LDMAQNLZ"},"agent_actions":{"view_html":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA","download_json":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA.json","view_paper":"https://pith.science/paper/LDMAQNLZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.03751&json=true","fetch_graph":"https://pith.science/api/pith-number/LDMAQNLZ2KIOKGXU7SXOF4HDNA/graph.json","fetch_events":"https://pith.science/api/pith-number/LDMAQNLZ2KIOKGXU7SXOF4HDNA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA/action/storage_attestation","attest_author":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA/action/author_attestation","sign_citation":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA/action/citation_signature","submit_replication":"https://pith.science/pith/LDMAQNLZ2KIOKGXU7SXOF4HDNA/action/replication_record"}},"created_at":"2026-07-05T11:15:51.400559+00:00","updated_at":"2026-07-05T11:15:51.400559+00:00"}