We discuss the adaptive full discretization of Gross-Pitaevskii equations with rotation term.
The model suggests to use a Laguerre--Hermite spatial discretization in a method of lines approach.
The resulting ODE system is propagated with higher-order splitting methods.
Based on theoretical error bounds for this full discretization,
asymptotically correct local error estimates employing either
embedding formulae or the defect correction principle enable adaptive time-stepping which
correctly reflects the solution behavior. Numerical examples illustrate the theoretical bounds and
demonstrate the practical performance of the methods.