In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.
