{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AZICHMRS4VBLPI5NQQRN74BOVD","short_pith_number":"pith:AZICHMRS","schema_version":"1.0","canonical_sha256":"065023b232e542b7a3ad8422dff02ea8ed137bdd73608eef78461f335efbe7cd","source":{"kind":"arxiv","id":"1709.03934","version":2},"attestation_state":"computed","paper":{"title":"Residual-based variational multiscale modeling in a discontinuous Galerkin framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dominik Schillinger, Sergio R. Turteltaub, Stein K.F. Stoter, Steven J. Hulshoff","submitted_at":"2017-09-12T16:17:30Z","abstract_excerpt":"We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we f"},"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":"1709.03934","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-12T16:17:30Z","cross_cats_sorted":[],"title_canon_sha256":"9e8c1bd1b23cb7c6495e8cd87480bc826868527048b73583f33c447d4733d342","abstract_canon_sha256":"b8c41f592e9cca2e1f4d5eaac07aaeec65b63cbef476f9665750593583f47f1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:54.586232Z","signature_b64":"ixretZvFsQvwBwoh5pWJnUrwQclxt7vOIowU196ItYVLpAahbrjyV0gD2jOWnf3d5WZ/5YGGPgIFCe6Y9i9nCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"065023b232e542b7a3ad8422dff02ea8ed137bdd73608eef78461f335efbe7cd","last_reissued_at":"2026-05-18T00:34:54.585429Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:54.585429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Residual-based variational multiscale modeling in a discontinuous Galerkin framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dominik Schillinger, Sergio R. Turteltaub, Stein K.F. Stoter, Steven J. Hulshoff","submitted_at":"2017-09-12T16:17:30Z","abstract_excerpt":"We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The obtained coarse-scale weak formulation includes two types of fine-scale contributions. The first type corresponds to a fine-scale volumetric term, which we formulate in terms of a residual-based model that also takes into account fine-scale effects at element interfaces. The second type consists of independent fine-scale terms at element interfaces, which we f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03934","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":""},"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":"1709.03934","created_at":"2026-05-18T00:34:54.585565+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03934v2","created_at":"2026-05-18T00:34:54.585565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03934","created_at":"2026-05-18T00:34:54.585565+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZICHMRS4VBL","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZICHMRS4VBLPI5N","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZICHMRS","created_at":"2026-05-18T12:31:08.081275+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/AZICHMRS4VBLPI5NQQRN74BOVD","json":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD.json","graph_json":"https://pith.science/api/pith-number/AZICHMRS4VBLPI5NQQRN74BOVD/graph.json","events_json":"https://pith.science/api/pith-number/AZICHMRS4VBLPI5NQQRN74BOVD/events.json","paper":"https://pith.science/paper/AZICHMRS"},"agent_actions":{"view_html":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD","download_json":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD.json","view_paper":"https://pith.science/paper/AZICHMRS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03934&json=true","fetch_graph":"https://pith.science/api/pith-number/AZICHMRS4VBLPI5NQQRN74BOVD/graph.json","fetch_events":"https://pith.science/api/pith-number/AZICHMRS4VBLPI5NQQRN74BOVD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD/action/storage_attestation","attest_author":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD/action/author_attestation","sign_citation":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD/action/citation_signature","submit_replication":"https://pith.science/pith/AZICHMRS4VBLPI5NQQRN74BOVD/action/replication_record"}},"created_at":"2026-05-18T00:34:54.585565+00:00","updated_at":"2026-05-18T00:34:54.585565+00:00"}