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

stability

converge nce.

optimal error estimates

Nonlinear Schr ̀ˆodinger equation

finite ele- ment method

Author

Mohammad Asadzadeh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Christoffer Standar

Chalmers, Mathematical Sciences

University of Gothenburg

Subject Categories

Mathematics

Roots

Basic sciences

More information

Created

1/3/2018 3