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.,
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.
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)
Electronic version of the publication:
Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen
Created from the Publication Database of the Vienna University of Technology.