Approximating the nonlinear Schrödinger equation by a two level linearly implicit finite element method
Preprint, 2017

Abstract. We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schrodi nger equation. We approximate the solution using a, local (non-uniform) two l evel scheme in time (see C. Besse [6] and [7]) combined with, an optimal, finite el ement strategy for the discretization in the spatial variable based on stud ies outlined as, e.g. in [2] and [10]. For the proposed fully discrete scheme, we show convergence both in L2 and H1 norms.

two level implicit schem e


converge nce.

optimal error estimates

Nonlinear Schr ̈odinger equation

finite ele- ment method


Mohammad Asadzadeh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Christoffer Standar

Chalmers, Mathematical Sciences

University of Gothenburg

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Basic sciences

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