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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
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.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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