Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems

摘要

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