Ainsworth, Mark; Rankin, Richard Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. (English) Zbl 1180.65141 SIAM J. Numer. Anal. 46, No. 6, 3207-3232 (2008). Summary: We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. Cited in 20 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:robust a posteriori error estimation; nonconforming finite element; numerical examples; linear second order elliptic problem PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{R. Rankin}, SIAM J. Numer. Anal. 46, No. 6, 3207--3232 (2008; Zbl 1180.65141) Full Text: DOI