{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AZ75DMBRXPNPKMHI2WNGMMVL5X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"40bda35558fdf8035d68c74c48d6ba410d3fc1680e6670f9b7914d4fca5bbe86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T10:47:01Z","title_canon_sha256":"377238e8dd8b22424906eafe393c57807c0153640326706bdb8bd1331d215bb4"},"schema_version":"1.0","source":{"id":"1504.01906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01906","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01906v2","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01906","created_at":"2026-05-18T00:53:15Z"},{"alias_kind":"pith_short_12","alias_value":"AZ75DMBRXPNP","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"AZ75DMBRXPNPKMHI","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"AZ75DMBR","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:5df4ba18cb013133d44ffa7474e8ca28a27e56988217adea9bea7bf88910d1f1","target":"graph","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker's technique introduced earlier by G. Baker ( SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equation, a posteriori error estimates of the displacement in L{\\infty}(L2)-norm for the semidiscrete scheme are derived under minimal regularity. Finally, a first order implicit-in-time discrete scheme i","authors_text":"Amiya K. Pani, Samir Karaa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T10:47:01Z","title":"On an a posteriori error analysis of mixed finite element Galerkin approximations to a second order wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01906","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:30762b8145a3706769fea45d68c49243781061c03bb4b64e9ea9b9a2618639cf","target":"record","created_at":"2026-05-18T00:53:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"40bda35558fdf8035d68c74c48d6ba410d3fc1680e6670f9b7914d4fca5bbe86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T10:47:01Z","title_canon_sha256":"377238e8dd8b22424906eafe393c57807c0153640326706bdb8bd1331d215bb4"},"schema_version":"1.0","source":{"id":"1504.01906","kind":"arxiv","version":2}},"canonical_sha256":"067fd1b031bbdaf530e8d59a6632abede0795ff592e5ba30b49262829bd3a4f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"067fd1b031bbdaf530e8d59a6632abede0795ff592e5ba30b49262829bd3a4f2","first_computed_at":"2026-05-18T00:53:15.993429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:15.993429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zpo3jm9FRfB2W9ami7OuskUFkW9muqtqJdUu4bd92fKDoQa8d/12XnQSLdcBnk6crfN5myabAp1D0ZQPTdArCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:15.993937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30762b8145a3706769fea45d68c49243781061c03bb4b64e9ea9b9a2618639cf","sha256:5df4ba18cb013133d44ffa7474e8ca28a27e56988217adea9bea7bf88910d1f1"],"state_sha256":"e3e68e14988b7f41363327e0f90a05406276ea65b30fd2e58bcdc93c75a09990"}