Ainsworth, Mark; Rankin, Richard Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. (English) Zbl 1208.65155 SIAM J. Numer. Anal. 47, No. 6, 4112-4141 (2010). This paper deals with a finite element approximations of a linear second-order elliptic problem on meshes containing an arbitrary number of levels of hanging nodes and comprised of triangular elements. An important part of analysis involves the construction of a bounded right inverse of the divergence operator. Fully computable upper bounds, as well as lower bounds are derived. Two numerical examples illustrating the theory are presented. Reviewer: Pavol Chocholatý (Bratislava) Cited in 15 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 Keywords:a posteriori error estimation; discontinuous Galerkin method; computable error bounds PDFBibTeX XMLCite \textit{M. Ainsworth} and \textit{R. Rankin}, SIAM J. Numer. Anal. 47, No. 6, 4112--4141 (2010; Zbl 1208.65155) Full Text: DOI