{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IW4II5SEXYTRE5ZAGRU2RK56AK","short_pith_number":"pith:IW4II5SE","schema_version":"1.0","canonical_sha256":"45b8847644be271277203469a8abbe028d35cdc5579525cc544e90a20094233e","source":{"kind":"arxiv","id":"1105.2112","version":2},"attestation_state":"computed","paper":{"title":"On stability of discretizations of the Helmholtz equation (extended version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jens Markus Melenk, Sofi Esterhazy","submitted_at":"2011-05-11T08:05:01Z","abstract_excerpt":"We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\\log k)$, and, additionally, appropriate mesh refinement is used near the"},"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":"1105.2112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-05-11T08:05:01Z","cross_cats_sorted":[],"title_canon_sha256":"6e00cd08a7eca4b7df9827a6523027f38f49362c81d636bc63b41ae50d601e58","abstract_canon_sha256":"4e1ef5ecfe2bf011ed6873df51c5510f5f98603788506b7a8232ff439200f18f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:11.201543Z","signature_b64":"Ni4c8UR06Lkp3Ig13LUc09NBdoSLh5Z4xQLgLhTeb77B2I2L34AiR6uKcz3sBli+VjtzZZCYgYNlTEkB21CPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45b8847644be271277203469a8abbe028d35cdc5579525cc544e90a20094233e","last_reissued_at":"2026-05-18T02:20:11.200791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:11.200791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On stability of discretizations of the Helmholtz equation (extended version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jens Markus Melenk, Sofi Esterhazy","submitted_at":"2011-05-11T08:05:01Z","abstract_excerpt":"We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\\log k)$, and, additionally, appropriate mesh refinement is used near the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2112","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":"1105.2112","created_at":"2026-05-18T02:20:11.200930+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2112v2","created_at":"2026-05-18T02:20:11.200930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2112","created_at":"2026-05-18T02:20:11.200930+00:00"},{"alias_kind":"pith_short_12","alias_value":"IW4II5SEXYTR","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IW4II5SEXYTRE5ZA","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IW4II5SE","created_at":"2026-05-18T12:26:32.869790+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/IW4II5SEXYTRE5ZAGRU2RK56AK","json":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK.json","graph_json":"https://pith.science/api/pith-number/IW4II5SEXYTRE5ZAGRU2RK56AK/graph.json","events_json":"https://pith.science/api/pith-number/IW4II5SEXYTRE5ZAGRU2RK56AK/events.json","paper":"https://pith.science/paper/IW4II5SE"},"agent_actions":{"view_html":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK","download_json":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK.json","view_paper":"https://pith.science/paper/IW4II5SE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2112&json=true","fetch_graph":"https://pith.science/api/pith-number/IW4II5SEXYTRE5ZAGRU2RK56AK/graph.json","fetch_events":"https://pith.science/api/pith-number/IW4II5SEXYTRE5ZAGRU2RK56AK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK/action/storage_attestation","attest_author":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK/action/author_attestation","sign_citation":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK/action/citation_signature","submit_replication":"https://pith.science/pith/IW4II5SEXYTRE5ZAGRU2RK56AK/action/replication_record"}},"created_at":"2026-05-18T02:20:11.200930+00:00","updated_at":"2026-05-18T02:20:11.200930+00:00"}