{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5MHTYQ64YB7NCRFNL5EZFOUZJM","short_pith_number":"pith:5MHTYQ64","schema_version":"1.0","canonical_sha256":"eb0f3c43dcc07ed144ad5f4992ba994b02e18b4ab3e663d95ddd265da914ec4e","source":{"kind":"arxiv","id":"1401.5150","version":1},"attestation_state":"computed","paper":{"title":"Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Waixiang Cao, Zhimin Zhang","submitted_at":"2014-01-21T02:28:31Z","abstract_excerpt":"In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We prove, for any polynomial degree $k$, that the numerical fluxes converge at a rate of $2k+1$ (or $2k+1/2$) for all mesh nodes and the domain average under some suitable initial discretization.\n  We further prove a $k+1$th superconvergence rate for the derivative approximation and a $k+2$th superconvergence rate for the function value approximation at the Radau points.\n  Numerical experiments demonstrate that in most c"},"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":"1401.5150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-01-21T02:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"477e37ea0987d4b6e5c78549c7e6562cd7fa73badbc64e6d60dd08f3b01e8052","abstract_canon_sha256":"ef0f03b62c637c44313e8ef8ccaf871d5d64db95a1d6f1073a45d8ac551abc86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.741446Z","signature_b64":"TGaIFgeI1wylAvPUqafww9Rw8rxIF89HmU1ziO5OfGiPdLVNb8Maj2IrZ1JePFTa39wc2ekNLkNdE4/u7X/bAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb0f3c43dcc07ed144ad5f4992ba994b02e18b4ab3e663d95ddd265da914ec4e","last_reissued_at":"2026-05-18T03:01:34.740986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.740986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Waixiang Cao, Zhimin Zhang","submitted_at":"2014-01-21T02:28:31Z","abstract_excerpt":"In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We prove, for any polynomial degree $k$, that the numerical fluxes converge at a rate of $2k+1$ (or $2k+1/2$) for all mesh nodes and the domain average under some suitable initial discretization.\n  We further prove a $k+1$th superconvergence rate for the derivative approximation and a $k+2$th superconvergence rate for the function value approximation at the Radau points.\n  Numerical experiments demonstrate that in most c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5150","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":""},"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":"1401.5150","created_at":"2026-05-18T03:01:34.741050+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.5150v1","created_at":"2026-05-18T03:01:34.741050+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5150","created_at":"2026-05-18T03:01:34.741050+00:00"},{"alias_kind":"pith_short_12","alias_value":"5MHTYQ64YB7N","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5MHTYQ64YB7NCRFN","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5MHTYQ64","created_at":"2026-05-18T12:28:14.216126+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/5MHTYQ64YB7NCRFNL5EZFOUZJM","json":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM.json","graph_json":"https://pith.science/api/pith-number/5MHTYQ64YB7NCRFNL5EZFOUZJM/graph.json","events_json":"https://pith.science/api/pith-number/5MHTYQ64YB7NCRFNL5EZFOUZJM/events.json","paper":"https://pith.science/paper/5MHTYQ64"},"agent_actions":{"view_html":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM","download_json":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM.json","view_paper":"https://pith.science/paper/5MHTYQ64","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.5150&json=true","fetch_graph":"https://pith.science/api/pith-number/5MHTYQ64YB7NCRFNL5EZFOUZJM/graph.json","fetch_events":"https://pith.science/api/pith-number/5MHTYQ64YB7NCRFNL5EZFOUZJM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM/action/storage_attestation","attest_author":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM/action/author_attestation","sign_citation":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM/action/citation_signature","submit_replication":"https://pith.science/pith/5MHTYQ64YB7NCRFNL5EZFOUZJM/action/replication_record"}},"created_at":"2026-05-18T03:01:34.741050+00:00","updated_at":"2026-05-18T03:01:34.741050+00:00"}