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Journal Articles Journal of Scientific Computing Year : 2023

A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials

Abstract

This paper is concerned with the numerical analysis of linear and nonlinear Schrödinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the solution in the linear cases, this is no longer true in general in the nonlinear case. We also study the rate of convergence of the planewave (Fourier) discretization method for computing numerical approximations of the solution.
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Dates and versions

hal-03692851 , version 1 (10-06-2022)
hal-03692851 , version 2 (30-03-2023)
hal-03692851 , version 3 (13-11-2023)

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Eric Cancès, Gaspard Kemlin, Antoine Levitt. A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials. Journal of Scientific Computing, 2023, 98 (1), pp.25. ⟨10.1007/s10915-023-02421-0⟩. ⟨hal-03692851v3⟩
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