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Using a variety of weak compactness techniques, including Chacon's biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to $0$. A key new technical tool in our analysis is a finite element counterpart of the Acerbi--Fusco Lipschitz truncation of Sobolev functions.<\/jats:p>","DOI":"10.1137\/120873133","type":"journal-article","created":{"date-parts":[[2013,3,21]],"date-time":"2013-03-21T12:18:59Z","timestamp":1363868339000},"page":"984-1015","source":"Crossref","is-referenced-by-count":53,"title":["Finite Element Approximation of Steady Flows of Incompressible Fluids with Implicit Power-Law-Like Rheology"],"prefix":"10.1137","volume":"51","author":[{"given":"Lars","family":"Diening","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Kreuzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Endre","family":"S\u00fcli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,3,21]]},"reference":[{"key":"atypb1","first-page":"1","volume-title":"Material Instabilities in Continuum Mechanics","author":"Acerbi E.","year":"1988"},{"key":"atypb2","volume-title":"Infinite Dimensional Analysis: A Hitchhiker's Guide","author":"Aliprantis C. 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