{"paper":{"title":"Optimal Error Estimates for Semidiscrete Galerkin approximations to the Equations of Motion Described by Kelvin-Voigt Viscoelastic Fluid Flow Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ambit K. Pany, Amiya K. Pani, Saumya Bajpai","submitted_at":"2015-11-28T23:49:19Z","abstract_excerpt":"In this paper, the finite element Galerkin method is applied to the equations of motion arising in the Kelvin-Voigt viscoelastic fluid flow model, when the forcing function is in $L^{\\infty}(L^2)$. Some a priori estimates for the exact solution, which are valid uniformly in time as $t\\mapsto \\infty$ and even uniformly in the retardation time $\\kappa$ as $\\kappa \\mapsto 0$, are derived. It is shown that the semidiscrete method admits a global attractor. Further, with the help of a priori bounds and Sobolev-Stokes projection, optimal error estimates for the velocity in $L^{\\infty}(L^2)$ and $L^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08947","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"}