In Cai and Zhang (2009), we introduced and analyzed an improved Zienkiewicz–Zhu (ZZ) estimator for the conforming linear finite element approximation to elliptic interface problems. The estimator is based on the piecewise “constant” flux recovery in the H(div;Ω) conforming finite element space. This paper extends the results of Cai and Zhang (2009) to diffusion problems with full diffusion tensor and to the flux recovery both in piecewise constant and piecewise linear H(div) space.
Cai, Z., He, C., & Zhang, S. (2017). Improved ZZ a posteriori error estimators for diffusion problems: Conforming linear elements. Computer Methods in Applied Mechanics and Engineering, 313, 433–449. https://doi.org/10.1016/j.cma.2016.10.006