{"paper":{"title":"A new mixed functional-probabilistic approach for finite element accuracy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Franck Assous, Jo\\\"el Chaskalovic","submitted_at":"2018-03-26T12:46:33Z","abstract_excerpt":"The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble-Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements $P_k$ and $P_m$, ($k < m$). Then, we analyze the asymptotic relation between these two probabilistic laws when the difference $m-k$ goes to infinity. New insights which qualified the relative accuracy in the case of high order finite elements are correspondingly obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09552","kind":"arxiv","version":8},"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"}