A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. In this paper we present a new technique that produces global a posteriori error estimates based on an optimized extrapolation method. The choice of the objective function as well as the representation of the unknown weight function in the extrapolation formula is discussed. This paper focuses on applications governed by the elliptic problem div(ρΔu)= f, with Dirichlet boundary conditions. Special attention is given to problems where the positive coefficient ρ exhibits large variations throughout the domain or f contains some singular source terms. These features are commonly encountered in physical problems including heat transfer with heterogeneous material properties and pressure solver in multiphase flows with large ratio of density between fluids.
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