{"paper":{"title":"Unfitted finite element methods using bulk meshes for surface partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Charles M. Elliott, Klaus Deckelnick, Thomas Ranner","submitted_at":"2013-12-10T18:19:45Z","abstract_excerpt":"In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\\Gamma \\subset \\mathbb{R}^{n+1}$, is embedded in a polyhedral domain in $\\mathbb R^{n+1}$ consisting of a union, $\\mathcal{T}_h$, of $(n+1)$-simplices. The finite element approximating space is based on continuous piece-wise linear finite element functions on $\\mathcal{T}_h$. Our first method is a sharp interface method, \\emph{SIF}, which uses the bulk finite element "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2905","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"}