{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JZSUVQAH7WWKZ6ITPOJ7N56Q6K","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":"74363487bd589a8297257a5c40a96eb52539236df49f6a60f34a400d801e031e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-13T15:00:40Z","title_canon_sha256":"236a01ec7f3ad86e6ce2fa4ea4252f04135ecd341a375c1c8cf0b2c8fa1f7ccd"},"schema_version":"1.0","source":{"id":"1811.05353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.05353","created_at":"2026-05-17T23:45:46Z"},{"alias_kind":"arxiv_version","alias_value":"1811.05353v2","created_at":"2026-05-17T23:45:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05353","created_at":"2026-05-17T23:45:46Z"},{"alias_kind":"pith_short_12","alias_value":"JZSUVQAH7WWK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JZSUVQAH7WWKZ6IT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JZSUVQAH","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:1ba73901a250123c10ae8de1b0833ade569e3fc0666d660196fcc648e77d6442","target":"graph","created_at":"2026-05-17T23:45:46Z","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 [Kopteva, Math. Comp., 2014] a counterexample of an anisotropic triangulation was given on which the exact solution has a second-order error of linear interpolation, while the computed solution obtained using linear finite elements is only first-order pointwise accurate. This example was given in the context of a singularly perturbed reaction-diffusion equation. In this paper, we present further examples of unanticipated pointwise convergence behaviour of Lagrange finite elements on anisotropic triangulations. In particular, we show that linear finite elements may exhibit lower than expecte","authors_text":"Natalia Kopteva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-13T15:00:40Z","title":"How accurate are finite elements on anisotropic triangulations in the maximum norm?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05353","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:fda77d0d2c3164997c9cd7ad443fe33ac38f0baffbaabcd84cad7a74b1047e63","target":"record","created_at":"2026-05-17T23:45:46Z","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":"74363487bd589a8297257a5c40a96eb52539236df49f6a60f34a400d801e031e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-13T15:00:40Z","title_canon_sha256":"236a01ec7f3ad86e6ce2fa4ea4252f04135ecd341a375c1c8cf0b2c8fa1f7ccd"},"schema_version":"1.0","source":{"id":"1811.05353","kind":"arxiv","version":2}},"canonical_sha256":"4e654ac007fdacacf9137b93f6f7d0f294420e3cd2bcaf15b8bf16c493f93c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e654ac007fdacacf9137b93f6f7d0f294420e3cd2bcaf15b8bf16c493f93c05","first_computed_at":"2026-05-17T23:45:46.581740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:46.581740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zTHgZC7npUzEg1BmFAV4nZAIjJQI+Sl51m0B6E8OckbNkWsJdpMyw4mLu/3vRXqxWoFVzXLIP+w3OmZBCInaDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:46.582370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.05353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fda77d0d2c3164997c9cd7ad443fe33ac38f0baffbaabcd84cad7a74b1047e63","sha256:1ba73901a250123c10ae8de1b0833ade569e3fc0666d660196fcc648e77d6442"],"state_sha256":"7e6827cff97fa248a443438c4439227687f61dfadeb4c04a0fce46612bf99929"}