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arXiv · 1711.00277

Approximating the nonlinear Schr\"odinger equation by a two level linearly implicit finite element method

Mohammad Asadzadeh·Christoffer Standar
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Abstract

We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6] and [7]) combined with, an optimal, finite element strategy for the discretization in the spatial variable based on studies outlined as, e.g. in [2] and [10]. For the proposed fully discrete scheme, we show convergence both in $L_2 $ and $H^1$ norms.

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Mohammad Asadzadeh, Christoffer Standar. 2017-11-01. Approximating the nonlinear Schr\"odinger equation by a two level linearly implicit finite element method. https://arxiv.org/abs/1711.00277

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