{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LOHJMXIPBOJD4GNO37P4SMPWDP","short_pith_number":"pith:LOHJMXIP","schema_version":"1.0","canonical_sha256":"5b8e965d0f0b923e19aedfdfc931f61bc95ec2b8563b57ffd72cc24e85ec4534","source":{"kind":"arxiv","id":"1703.03561","version":3},"attestation_state":"computed","paper":{"title":"Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hendrik Ranocha, Jan Glaubitz, Philipp \\\"Offner","submitted_at":"2017-03-10T07:32:59Z","abstract_excerpt":"In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equations, which can be solved by several numerical methods. Here, we apply the correction procedure via reconstruction (CPR) using summation-by-parts operators. We focus especially on stability, which is proven for CPR methods and the systems arising from the PC approach. Due to the usage of split-forms, the major challenge is to construct entropy stable numerical fluxes. For the first time, such numerical fluxes are constr"},"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":"1703.03561","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-10T07:32:59Z","cross_cats_sorted":[],"title_canon_sha256":"82e1aa9764132356659c08d7e7a89910c264710f96fbf9575fd3e3302e87f383","abstract_canon_sha256":"f839d44768c210e71c76faf282534d615b285d26f32c91f5e949e57cc75f1fce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:01.289100Z","signature_b64":"cKpmqKPKBqLs+RSJ6onEZ7rMNCj3C+E8eEGJNeirsIVmifqc5eaqfL0rW+cVfN+d75JOKznSfef0xczqA6p0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b8e965d0f0b923e19aedfdfc931f61bc95ec2b8563b57ffd72cc24e85ec4534","last_reissued_at":"2026-05-17T23:55:01.288522Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:01.288522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hendrik Ranocha, Jan Glaubitz, Philipp \\\"Offner","submitted_at":"2017-03-10T07:32:59Z","abstract_excerpt":"In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equations, which can be solved by several numerical methods. Here, we apply the correction procedure via reconstruction (CPR) using summation-by-parts operators. We focus especially on stability, which is proven for CPR methods and the systems arising from the PC approach. Due to the usage of split-forms, the major challenge is to construct entropy stable numerical fluxes. For the first time, such numerical fluxes are constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03561","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":""},"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":"1703.03561","created_at":"2026-05-17T23:55:01.288587+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03561v3","created_at":"2026-05-17T23:55:01.288587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03561","created_at":"2026-05-17T23:55:01.288587+00:00"},{"alias_kind":"pith_short_12","alias_value":"LOHJMXIPBOJD","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LOHJMXIPBOJD4GNO","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LOHJMXIP","created_at":"2026-05-18T12:31:28.150371+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/LOHJMXIPBOJD4GNO37P4SMPWDP","json":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP.json","graph_json":"https://pith.science/api/pith-number/LOHJMXIPBOJD4GNO37P4SMPWDP/graph.json","events_json":"https://pith.science/api/pith-number/LOHJMXIPBOJD4GNO37P4SMPWDP/events.json","paper":"https://pith.science/paper/LOHJMXIP"},"agent_actions":{"view_html":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP","download_json":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP.json","view_paper":"https://pith.science/paper/LOHJMXIP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03561&json=true","fetch_graph":"https://pith.science/api/pith-number/LOHJMXIPBOJD4GNO37P4SMPWDP/graph.json","fetch_events":"https://pith.science/api/pith-number/LOHJMXIPBOJD4GNO37P4SMPWDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP/action/storage_attestation","attest_author":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP/action/author_attestation","sign_citation":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP/action/citation_signature","submit_replication":"https://pith.science/pith/LOHJMXIPBOJD4GNO37P4SMPWDP/action/replication_record"}},"created_at":"2026-05-17T23:55:01.288587+00:00","updated_at":"2026-05-17T23:55:01.288587+00:00"}