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In \cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu(ZZ) estimator for the conforming linear finite element approximation toelliptic interface problems. The estimator is based on the piecewise "constant"flux recovery in the $H(div;\Omega)$ conforming finite element space. Thispaper extends the results of \cite{CaZh:09} to diffusion problems with fulldiffusion tensor and to the flux recovery both in piecewise constant andpiecewise linear $H(div)$ space.

Improved ZZ A Posteriori Error Estimators for Diffusion Problems: Conforming Linear Elements