A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrodinger equations

In this Note, we propose a new method, based on perturbation theory, to post-process the planewave approximation of the eigenmodes of periodic Schrodinger operators. We then use this post-processing to construct an accurate a posteriori estimator for the approximations of the (nonlinear) Gross-Pitaevskii equation, valid at each step of a self-consistent procedure. This allows us to design an adaptive algorithm for solving the Gross-Pitaevskii equation, which automatically refines the discretization along the convergence of the iterative process, by means of adaptive stopping criteria. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.