{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PX2ICX7T6JUSXRWOFG5CVOT3I2","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":"7f862313a9c8e3dff8f7afc2aecce8dd30d3c7169dec90e20703f3e1ab4f2e62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T14:42:39Z","title_canon_sha256":"5d34e8d9eaccb8c8d935fc632a49a847907ecee1747fb7afe5d4a35e64517e2e"},"schema_version":"1.0","source":{"id":"1505.03032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03032","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03032v2","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03032","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"PX2ICX7T6JUS","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PX2ICX7T6JUSXRWO","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PX2ICX7T","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:a402326e9e4f941b125be9e43c1d24106201e139c7accc726c991658378a4c60","target":"graph","created_at":"2026-05-18T01:36:47Z","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":"The solutions of elliptic problems with a Dirac measure in right-hand side are not H1 and therefore the convergence of the finite element solutions is suboptimal. Graded meshes are standard remedy to recover quasi-optimality, namely optimality up to a log-factor, for low order finite elements in L2-norm. Optimal (or quasi-optimal for the lowest order case) convergence has been shown in L2-seminorm, where the L2-seminorm is defined as the L2-norm on a subdomain which excludes the singularity. Here we show a quasi-optimal convergence for the Hs-seminorm, s \\textgreater{} 0, and an optimal conver","authors_text":"Astrid Decoene (LM-Orsay), Lo\\\"ic Lacouture (LM-Orsay), S\\'ebastien Martin (MAP5), Silvia Bertoluzza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T14:42:39Z","title":"Local Error Estimates of the Finite Element Method for an Elliptic Problem with a Dirac Source Term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03032","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":"sha256:10bc8401bdf8447a924d3b343db3ac616e8c3b34a443a6f144050c205c03905f","target":"record","created_at":"2026-05-18T01:36:47Z","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":"7f862313a9c8e3dff8f7afc2aecce8dd30d3c7169dec90e20703f3e1ab4f2e62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-05-12T14:42:39Z","title_canon_sha256":"5d34e8d9eaccb8c8d935fc632a49a847907ecee1747fb7afe5d4a35e64517e2e"},"schema_version":"1.0","source":{"id":"1505.03032","kind":"arxiv","version":2}},"canonical_sha256":"7df4815ff3f2692bc6ce29ba2aba7b46a2e4cae73f254722031ed3901b4bfefe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7df4815ff3f2692bc6ce29ba2aba7b46a2e4cae73f254722031ed3901b4bfefe","first_computed_at":"2026-05-18T01:36:47.806350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:47.806350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ru6fyOu0oC+oIrqop6csxKbWsvgBq78/y879QSQ5SLZueorCil1C73unprV8da77rRlcxdV4L0AD1GaR491GCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:47.807023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10bc8401bdf8447a924d3b343db3ac616e8c3b34a443a6f144050c205c03905f","sha256:a402326e9e4f941b125be9e43c1d24106201e139c7accc726c991658378a4c60"],"state_sha256":"260c757db6359a0d8bdf2743c4d87d3e4184e0884bba20e9f4ce32a09e57be6f"}