In this talk we consider a post-processing of planewave approximations for DFT Kohn-Sham models by considering the exact solution as a perturbation of the discrete solution. Applying then Kato’s perturbation theory leads to computable corrections with a provable increase of the convergence rate in the asymptotic range. I first focus on the key-features of this post-processing by carefully analyzing the Gross-Pitaevskii equation that serves as a toy problem before I discuss to the DFT Kohn-Sham models. Finally some numerical illustrations are presented. If time permitting, I will also discuss some recent advances of a posteriori estimates for the Gross-Pitaevskii equation.