In this talk I will present some recent results on aposteriori error estimation for linear and nonlinear Schrodinger equations. We use finite element discretizations and the Crank Nicolson time stepping scheme. For the derivation of the estimates we use the reconstruction technique and linear and nonlinear stability arguments as in the continuous problem. Based on these aposteriori estimators we further design and analyse a time-space adaptive algorithm. Various numerical experiments verify and complement our theoretical results.
This is a joint work with I. Kyza, Univ. of Dundee, UK.