{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:KDWKTZRLVFGYKADKNX3RYKFB2J","short_pith_number":"pith:KDWKTZRL","schema_version":"1.0","canonical_sha256":"50eca9e62ba94d85006a6df71c28a1d2551802ebcfc72727b5fcfa2cd76eec17","source":{"kind":"arxiv","id":"2009.13139","version":2},"attestation_state":"computed","paper":{"title":"Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Gregor J Gassner, Hendrik Ranocha","submitted_at":"2020-09-28T08:38:28Z","abstract_excerpt":"Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible Euler equations. The issue is related to missing local linear stability, i.e. the stability of the discretization towards perturbations added to a stable base flow. This is strongly related to an anti-diffusion mechanism, that is inherent in entropy-conserving two-point fluxes, which are a key ingredient for the high-order discontinuous Galerkin extension. In "},"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":"2009.13139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-09-28T08:38:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fd0af304cb0852354524a04d80479e5d1da2c80caf35c291803ad42bbaca4d83","abstract_canon_sha256":"88cbd88defea91c38cf02e257b2e0f03540b84a1b543075ea996d691916dc0e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:02:08.894545Z","signature_b64":"oEKhe7N1ij2miOlawEp8cDr5YRzhIcIS2jx1evsuYtixeYAK1qzmXY7eKoeB3oA0i27A1Zr4TYH9jJnMMF8/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50eca9e62ba94d85006a6df71c28a1d2551802ebcfc72727b5fcfa2cd76eec17","last_reissued_at":"2026-07-05T03:02:08.894144Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:02:08.894144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Gregor J Gassner, Hendrik Ranocha","submitted_at":"2020-09-28T08:38:28Z","abstract_excerpt":"Recently, it was discovered that the entropy-conserving/dissipative high-order split-form discontinuous Galerkin discretizations have robustness issues when trying to solve the simple density wave propagation example for the compressible Euler equations. The issue is related to missing local linear stability, i.e. the stability of the discretization towards perturbations added to a stable base flow. This is strongly related to an anti-diffusion mechanism, that is inherent in entropy-conserving two-point fluxes, which are a key ingredient for the high-order discontinuous Galerkin extension. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13139","kind":"arxiv","version":2},"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/2009.13139/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":"2009.13139","created_at":"2026-07-05T03:02:08.894205+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.13139v2","created_at":"2026-07-05T03:02:08.894205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13139","created_at":"2026-07-05T03:02:08.894205+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDWKTZRLVFGY","created_at":"2026-07-05T03:02:08.894205+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDWKTZRLVFGYKADK","created_at":"2026-07-05T03:02:08.894205+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDWKTZRL","created_at":"2026-07-05T03:02:08.894205+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.21427","citing_title":"Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods","ref_index":53,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J","json":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J.json","graph_json":"https://pith.science/api/pith-number/KDWKTZRLVFGYKADKNX3RYKFB2J/graph.json","events_json":"https://pith.science/api/pith-number/KDWKTZRLVFGYKADKNX3RYKFB2J/events.json","paper":"https://pith.science/paper/KDWKTZRL"},"agent_actions":{"view_html":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J","download_json":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J.json","view_paper":"https://pith.science/paper/KDWKTZRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.13139&json=true","fetch_graph":"https://pith.science/api/pith-number/KDWKTZRLVFGYKADKNX3RYKFB2J/graph.json","fetch_events":"https://pith.science/api/pith-number/KDWKTZRLVFGYKADKNX3RYKFB2J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J/action/storage_attestation","attest_author":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J/action/author_attestation","sign_citation":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J/action/citation_signature","submit_replication":"https://pith.science/pith/KDWKTZRLVFGYKADKNX3RYKFB2J/action/replication_record"}},"created_at":"2026-07-05T03:02:08.894205+00:00","updated_at":"2026-07-05T03:02:08.894205+00:00"}