Braess, Dietrich; Verfürth, R. A posteriori error estimators for the Raviart-Thomas element. (English) Zbl 0866.65071 SIAM J. Numer. Anal. 33, No. 6, 2431-2444 (1996). This paper is concerned with the development of a posteriori error estimators for the Raviart-Thomas element which is really powerful for mixed finite element methods. The difficulties met in such a development are:– the \(H(\text{div},\Omega)\)-norm is an anisotropic norm since it refers to differential operators of different orders;– the traces of \(H(\text{div},\Omega)\)-functions are only in \(H^{-1/2}\).The authors obtain and analyze reliable and efficient residual error estimators for the error measured in mesh-dependent norms.This paper includes all the proofs and is nicely written. Reviewer: M.Bernadou (Le Chesnay) Cited in 2 ReviewsCited in 92 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:mesh-dependent norms; Poisson equation; error estimators; Raviart-Thomas element; mixed finite element methods PDFBibTeX XMLCite \textit{D. Braess} and \textit{R. Verfürth}, SIAM J. Numer. Anal. 33, No. 6, 2431--2444 (1996; Zbl 0866.65071) Full Text: DOI