Type: Article
Publication Date: 2016-09-14
Citations: 7
DOI: https://doi.org/10.1051/m2an/2016059
Operator splitting methods combined with finite element spatial discretizations are studied for time-dependent nonlinear Schrödinger equations. In particular, the Schrödinger–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.