Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis

Given a flux or stress approximation ph from a low-order finite element simulation of an elliptic boundary value problem, averaging or (gradient-)recovery techniques aim the computation of an improved approximation Aph by a (simple) post processing of ph. For instance, frequently named after Zienkiewicz and Zhu, Aph is the elementwise interpolation of the nodal values (Aph)(z) obtained as the integral mean of ph on a neighbourhood of z. This paper gives an overview over old

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