  We provide a posteriori error estimates in the $L^\infty(L^2)-$norm for
relaxation time discrete and fully discrete schemes for a class of evolution
nonlinear Schr\"odinger equations up to the critical exponent. In particular
for the discretization in time we use the relaxation Crank-Nicolson-type scheme
introduced by Besse in \cite{Besse}. For the discretization in space we use
finite element spaces that are allowed to change between time steps. The
estimates are obtained using the reconstruction technique. Through this
technique the problem is converted to a perturbation of the original partial
differential equation and this makes it possible to use nonlinear stability
arguments as in the continuous problem. In particular, main ingredients we use
in our analysis are the Gagliardo-Nirenberg inequality and the two conservation
laws (mass and energy conservation) of the continuous problem. Numerical
results illustrate that the estimates are indeed of optimal order of
convergence.
