  The contribution of this paper contains two parts: first, we prove a
supercloseness result for the partially penalized immersed finite element
(PPIFE) method in [T. Lin, Y. Lin, and X. Zhang, SIAM J. Numer. Anal., 53
(2015), 1121--1144]; then based on the supercloseness result, we show that the
gradient recovery method proposed in our previous work [H. Guo and X. Yang,
arXiv: 1608.00063] can be applied to the PPIFE method and the recovered
gradient converges to the exact gradient with a superconvergent rate
$\mathcal{O}(h^{3/2})$. Hence, the gradient recovery method provides an
asymptotically exact a posteriori error estimator for the PPIFE method. Several
numerical examples are presented to verify our theoretical result.
