{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MFFLW4SRA4YAK6FATQD2RZVMJK","short_pith_number":"pith:MFFLW4SR","schema_version":"1.0","canonical_sha256":"614abb725107300578a09c07a8e6ac4a876df6bead5544a5c00f9d2f727a0e75","source":{"kind":"arxiv","id":"1110.4046","version":1},"attestation_state":"computed","paper":{"title":"Crank-Nicolson Finite Element Discretizations for a 2D Linear Schr\\\"odinger-Type Equation Posed in a Noncylindrical Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"D. C. Antonopoulou, G. D. Karali, G. E. Zouraris, M. Plexousakis","submitted_at":"2011-10-18T16:30:43Z","abstract_excerpt":"Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\\\"odinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initial- and boundary-value problem is transformed into an equivalent one posed on a rectangular domain and is approximated by fully discrete, $L^2$-stable, finite element, Crank--Nicolson type schemes. We prove a global elliptic regularity theorem for complex elliptic boundary value"},"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":"1110.4046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-18T16:30:43Z","cross_cats_sorted":[],"title_canon_sha256":"c26d999f01a2d2e083a911ffc131f40197bfb0dce9e32e1aa5e38378c89d9940","abstract_canon_sha256":"0aaf79011f58ffb9d82a3e998e72994fdb81b501e3dfd78ffa45ea9c55997646"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:47.464924Z","signature_b64":"KYejukhnb9tusGqDVqLTZX/Ijo094LoVR7VoQ6u3DOEMIL5W74Zz596JbBPdTV/YUo6QQMYb5Pd9qj+nuOrQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"614abb725107300578a09c07a8e6ac4a876df6bead5544a5c00f9d2f727a0e75","last_reissued_at":"2026-05-18T04:10:47.464483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:47.464483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crank-Nicolson Finite Element Discretizations for a 2D Linear Schr\\\"odinger-Type Equation Posed in a Noncylindrical Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"D. C. Antonopoulou, G. D. Karali, G. E. Zouraris, M. Plexousakis","submitted_at":"2011-10-18T16:30:43Z","abstract_excerpt":"Motivated by the paraxial narrow-angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schr\\\"odinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initial- and boundary-value problem is transformed into an equivalent one posed on a rectangular domain and is approximated by fully discrete, $L^2$-stable, finite element, Crank--Nicolson type schemes. We prove a global elliptic regularity theorem for complex elliptic boundary value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4046","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":"1110.4046","created_at":"2026-05-18T04:10:47.464554+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.4046v1","created_at":"2026-05-18T04:10:47.464554+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4046","created_at":"2026-05-18T04:10:47.464554+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFFLW4SRA4YA","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFFLW4SRA4YAK6FA","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFFLW4SR","created_at":"2026-05-18T12:26:34.985390+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/MFFLW4SRA4YAK6FATQD2RZVMJK","json":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK.json","graph_json":"https://pith.science/api/pith-number/MFFLW4SRA4YAK6FATQD2RZVMJK/graph.json","events_json":"https://pith.science/api/pith-number/MFFLW4SRA4YAK6FATQD2RZVMJK/events.json","paper":"https://pith.science/paper/MFFLW4SR"},"agent_actions":{"view_html":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK","download_json":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK.json","view_paper":"https://pith.science/paper/MFFLW4SR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.4046&json=true","fetch_graph":"https://pith.science/api/pith-number/MFFLW4SRA4YAK6FATQD2RZVMJK/graph.json","fetch_events":"https://pith.science/api/pith-number/MFFLW4SRA4YAK6FATQD2RZVMJK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK/action/storage_attestation","attest_author":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK/action/author_attestation","sign_citation":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK/action/citation_signature","submit_replication":"https://pith.science/pith/MFFLW4SRA4YAK6FATQD2RZVMJK/action/replication_record"}},"created_at":"2026-05-18T04:10:47.464554+00:00","updated_at":"2026-05-18T04:10:47.464554+00:00"}