{"paper":{"title":"Penalty method with Crouzeix-Raviart approximation for the Stokes equations under slip boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Guanyu Zhou, Issei Oikawa, Takahito Kashiwabara","submitted_at":"2018-09-25T13:28:09Z","abstract_excerpt":"The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain $\\Omega \\subset \\mathbb R^N \\, (N=2,3)$. We propose a finite element scheme based on the nonconforming P1/P0 approximation (Crouzeix-Raviart approximation) combined with a penalty formulation and with reduced-order numerical integration in order to address the essential boundary condition $u \\cdot n_{\\partial\\Omega} = g$ on $\\partial\\Omega$. Because the original domain $\\Omega$ must be approximated by a polygonal (or polyhedral) domain $\\Omega_h$ before applying the finite element method,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09464","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"}