{"paper":{"title":"A mass conserving mixed stress formulation for the Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jay Gopalakrishnan, Joachim Sch\\\"oberl, Philip L. Lederer","submitted_at":"2018-06-19T12:01:55Z","abstract_excerpt":"We propose a new discretization of a mixed stress formulation of the Stokes equations. The velocity $u$ is approximated with $H(\\operatorname{div})$-conforming finite elements providing exact mass conservation. While many standard methods use $H^1$-conforming spaces for the discrete velocity, $H(\\operatorname{div})$-conformity fits the considered variational formulation in this work. A new stress-like variable $\\sigma$ equalling the gradient of the velocity is set within a new function space $H(\\operatorname{curl} \\operatorname{div})$. New matrix-valued finite elements having continuous \"norma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07173","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"}