  We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality
of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming
approximations of the Poisson problem to nonconforming Crouzeix-Raviart
approximations of the Poisson and the Stokes problem in 2D. As a consequence,
we obtain instance optimality of an AFEM with a modified maximum marking
strategy.
