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

Abstract : In this Note, we propose a new method, based on perturbation theory, to post-process the planewave approximation of the eigenmodes of periodic Schrödinger 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.
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Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík. A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations. Comptes Rendus Mathématique, Elsevier Masson, 2014, 352 (11), pp.941-946. ⟨10.1016/j.crma.2014.09.014⟩. ⟨hal-00994568⟩

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