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arXiv · 1605.00437

Convergence of a Strang splitting finite element discretization for the Schr\"odinger-Poisson equation

Winfried Auzinger·Thomas Kassebacher·Othmar Koch·Mechthild Thalhammer
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Abstract

Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schr\"odinger equations. In particular, the Schr\"odinger-Poisson equation under homogeneous Dirichlet boundary conditions on a finite domain is considered. A rigorous stability and error analysis is carried out for the second-order Strang splitting method and conforming polynomial finite element discretizations. For sufficiently regular solutions the classical orders of convergence are retained, that is, second-order convergence in time and polynomial convergence in space is proven. The established convergence result is confirmed and complemented by numerical illustrations.

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Winfried Auzinger, Thomas Kassebacher, Othmar Koch, Mechthild Thalhammer. 2016-05-02. Convergence of a Strang splitting finite element discretization for the Schr\"odinger-Poisson equation. https://arxiv.org/abs/1605.00437

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