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Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The discrete minimal least-squares functional $LS(f;U)$ is equivalent to the squared error $|| u-U ||^2$ in least-squares finite element methods and so leads to an embedded reliable and efficient a posteriori error control. This paper enfolds a spectral analysis to prove that this natural error estimator is asymptotically exact in the sense that the ratio $LS(f;U)\/||u-U||^2$ tends to one as the underlying mesh-size tends to zero for the Poisson model problem, the Helmholtz equation, the linear elasticity, and the time-harmonic Maxwell equations with all kinds of conforming discretizations. Some knowledge about the continuous and the discrete eigenspectrum allows for the computation of a guaranteed error bound $C(\\mathcal{T}) LS(f;U)$ with a reliability constant $C(\\mathcal{T}) \\leq 1\/\\alpha$ smaller than that from the coercivity constant $\\alpha$. Numerical examples confirm the estimates and illustrate the performance of the novel guaranteed error bounds with improved efficiency.<\/jats:p>","DOI":"10.1137\/17m1125972","type":"journal-article","created":{"date-parts":[[2018,7,3]],"date-time":"2018-07-03T13:40:49Z","timestamp":1530625249000},"page":"2008-2028","source":"Crossref","is-referenced-by-count":14,"title":["Asymptotic Exactness of the Least-Squares Finite Element Residual"],"prefix":"10.1137","volume":"56","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Storn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,7,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-016-0822-1"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290443353X"},{"key":"atypb3","volume-title":"Appl. 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