{"paper":{"title":"Two 11-node nonconforming triangular prism elements for 3D elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Xinchen Zhou, Xin Fan, Zhaoliang Meng, Zhongxuan Luo","submitted_at":"2018-11-19T05:39:02Z","abstract_excerpt":"This work introduces two 11-node triangular prism elements for 3D elliptic problems. The degrees of freedom (DoFs) of both elements are at the vertices and face centroids of a prism cell. The first element is $H^1$-nonconforming and works for second order problems, which achieves a second order convergence rate in discrete $H^1$-norm. The other is $H^2$-nonconforming and solves fourth order problems, with a first order convergence rate in discrete $H^2$-norm. Numerical examples verify our theoretical results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07507","kind":"arxiv","version":1},"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"}