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Publications in Scientific Journals:

W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer:
"Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation";
M2AN Math. Model. Numer. Anal., 51 (2017), 1; 1245 - 1278.



English abstract:
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.

Keywords:
Nonlinear Schrödinger equations, Operator splitting methods, Finite element discretization, Stability, Local error, Convergenc


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1051/m2an/2016059

Electronic version of the publication:
https://doi.org/10.1051/m2an/2016059



Related Projects:
Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen


Created from the Publication Database of the Vienna University of Technology.