{"paper":{"title":"A penalty finite element method for a fluid system posed on embedded surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Maxim A. Olshanskii, Vladimir Yushutin","submitted_at":"2018-06-18T09:08:06Z","abstract_excerpt":"The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\\Gamma\\subset\\R^3$. The method needs a shape regular tetrahedra mesh in $\\mathbb{R}^3$ to discretize equations on the surface, which can cut through this mesh in a fairly arbitrary way. Stability and error analysis of the fully discrete (in space and in time) scheme is given. The tangentiality condition for the velocity field on $\\Gamma$ is enforced weakly by a penalty term. The paper studies both theoretically and numerically the dependence of the error on the penalty parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06557","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"}