Chen, Long; Wang, Junping; Ye, Xiu A posteriori error estimates for weak Galerkin finite element methods for second order elliptic problems. (English) Zbl 1307.65153 J. Sci. Comput. 59, No. 2, 496-511 (2014). The authors are concerned with the development of residual-type a posteriori error estimators for a recently introduced weak Galerkin finite element method, i.e., in which differential operators are approximated by weak forms as distributions. Moreover, they provide an a posteriori error estimator, together with a theoretical upper and lower bound. Reviewer: Constantin Popa (Constanţa) Cited in 57 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 Keywords:discrete weak gradient; second-order elliptic problems; a posteriori error estimate; weak Galerkin finite element method Software:iFEM PDFBibTeX XMLCite \textit{L. Chen} et al., J. Sci. Comput. 59, No. 2, 496--511 (2014; Zbl 1307.65153) Full Text: DOI References: [1] Ainsworth, M.: Robust a posteriori error estimation for nonconforming finite element approximation. SIAM J. Numer. Anal. 42(6), 2320-2341 (2005) · Zbl 1085.65102 · doi:10.1137/S0036142903425112 [2] Alonso, A.: Error estimators for a mixed method. Numer. Math. 74(4), 385-395 (1996) · Zbl 0866.65068 · doi:10.1007/s002110050222 [3] Carstensen, C.: A posteriori error estimate for the mixed finite element method. Math. 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