Hannukainen, A.; Korotov, S. Techniques for a posteriori error estimation in terms of linear functionals for elliptic type boundary value problems. (English) Zbl 1092.65097 Far East J. Appl. Math. 21, No. 3, 289-304 (2005). Summary: A uniform scheme for a posteriori estimation of computational errors in terms of linear functionals for elliptic type boundary value problems is presented. In the framework of this scheme easy-to-code construction of error estimators and error indicators is proposed. Main properties of estimators and indicators obtained are discussed and their effectivity is demonstrated in numerical tests. Cited in 3 Documents MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs Keywords:local errors; differential equation of elliptic type; two-sided error estimates; finite element method; error indication; superconvergence; gradient averaging PDFBibTeX XMLCite \textit{A. Hannukainen} and \textit{S. Korotov}, Far East J. Appl. Math. 21, No. 3, 289--304 (2005; Zbl 1092.65097)