{"paper":{"title":"Penalty method with P1/P1 finite element 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":"2015-05-25T05:02:11Z","abstract_excerpt":"We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied to address the essential boundary condition $u\\cdot n = g$ on $\\partial\\Omega$, which avoids a variational crime and simultaneously facilitates the numerical implementation. We give $O(h^{1/2} + \\epsilon^{1/2} + h/\\epsilon^{1/2})$-error estimate for velocity and pressure in the energy norm, where $h$ and $\\epsilon$ denote the discretization parameter and the penalty parameter, respectively. In the two-dimensional ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06540","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"}