{"paper":{"title":"Optimal error estimate for semi-implicit space-time discretization for the equations describing incompressible generalized Newtonian fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lars Diening, Luigi C. Berselli, Michael Ruzicka","submitted_at":"2013-07-29T13:47:04Z","abstract_excerpt":"In this paper we study the numerical error arising in the space-time approximation of unsteady generalized Newtonian fluids which possess a stress-tensor with $(p,\\delta)$-structure. A semi-implicit time-discretization scheme coupled with conforming inf-sup stable finite element space discretization is analyzed. The main result, which improves previous suboptimal estimates as those in [A. Prohl, and M. Ruzicka, SIAM J. Numer. Anal., 39 (2001), pp. 214--249] is the optimal $O(k+h)$ error-estimate valid in the range $p\\in (3/2,2]$, where $k$ and $h$ are the time-step and the mesh-size, respectiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7578","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"}