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W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer:
"Adaptive time-splitting FEM discretization of the Schrödinger-Poisson equation";
Vortrag: Workshop on modern numerical methods in quantum dynamics, Warschau (eingeladen); 20.03.2017 - 22.03.2017.

We discuss the adaptive numerical solution of the Schr¨odinger-Poisson equation on a
truncated finite domain with an underlying space discretization by conforming piecewise
polynomial finite elements, where we truncate to a sufficiently large finite domain and
impose homogeneous Dirichlet boundary conditions. The motivation for this approach is
the possibility to treat the Poisson equation separately by dedicated solvers for the arising
linear equations. The classical convergence orders in both the time and space discretization
are established theoretically under natural assumptions on the regularity of the exact
solution and illustrated by numerical experiments. Adaptive time-stepping relying on a
defect-based error estimator is shown to correctly reflect the solution behaviour.