{"paper":{"title":"Nonconforming P1 elements on distorted triangulations: Lower bounds for the discrete energy norm error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Peter Oswald","submitted_at":"2016-07-20T14:55:13Z","abstract_excerpt":"Compared to conforming P1 finite elements, nonconforming P1 finite element discretizations are thought to be less sensitive to the appearance of distorted triangulations. E.g., optimal-order discrete $H^1$ norm best approximation error estimates for $H^2$ functions hold for arbitrary triangulations. However, similar estimates for the error of the Galerkin projection for second-order elliptic problems show a dependence on the maximum angle of all triangles in the triangulation. We demonstrate on the example of a special family of distorted triangulations that this dependence is essential, and d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05983","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"}