{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:24:15Z","timestamp":1787333055579,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Rheological behavior of certain non\u2010Newtonian fluids in engineering sciences is often modeled by power law ansatzes with $p \\leq 2$. So far, existing numerical analysis for local strong solutions studies a fully implicit time discretization and find only restricted ranges of admissible p\u2019s for corresponding error estimates [A. Prohl and M. R\u016f\u017ei\u010dka, SIAM J. Numer. Anal., 39 (2001), pp. 214\u2013249]; different nonlinear stabilization strategies which allow a corresponding error analysis for smaller p\u2019s are examined in [L. Diening, Theoretical and Numerical Results for Electrorheological Fluids, Ph.D. thesis, University of Freiburg, Freiburg, Germany, 2002] and [L. Diening, A. Prohl, and M. R\u016f\u017ei\u010dka, in Nonlinear Problems in Mathematical Physics and Related Topics, II, Kluwer\/Plenum, New York, 2002, pp. 89\u2013118]. In the present paper, a semi\u2010implicit time discretization scheme is proposed, and error estimates apply to the extended range $p \\in (\\frac{3}{2} ,2]$. The key analytical tool is a new Gronwall\u2010type inequality.<\/jats:p>","DOI":"10.1137\/050634335","type":"journal-article","created":{"date-parts":[[2006,8,24]],"date-time":"2006-08-24T15:29:50Z","timestamp":1156433390000},"page":"1172-1190","source":"Crossref","is-referenced-by-count":22,"title":["Semi\u2010implicit Euler Scheme for Generalized Newtonian Fluids"],"prefix":"10.1137","volume":"44","author":[{"given":"Lars","family":"Diening","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Prohl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"R\u016f\u017ei\u010dka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,6,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"H. 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Rajagopal,\n                      Mechanics of non\u2010Newtonian fluids\n                      , in Recent Developments in Theoretical Fluid Mechanics, Pitman Res. Notes Math. Ser. 291, G. P. Galdi and J. Ne\u010das, eds., Longman, Harlow, UK, 1993, pp. 129\u2013162.","DOI":"10.1201\/9781003417026-5"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(97)00391-X"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s10492-004-6432-8"},{"key":"R17","unstructured":"G. Th\u00e4ter,\n                      Natural Convection, Dissipation & Power\u2010Law Rheology: Mathematical Models & Results\n                      , Habilitation Thesis, University of Hannover, Hannover, Germany, 2003."},{"key":"R18","unstructured":"J. Wolf,\n                      Existence of weak solutions to the equations of nonstationary motion of non\u2010Newtonian fluids with shear\u2010dependent viscosity\n                      , J. Math. 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