Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems
Provides theoretical optimality guarantees for nonconforming adaptive methods, benefiting numerical analysts working on adaptive finite element methods.
The paper extends instance optimality of adaptive finite element methods with a modified maximum marking strategy from conforming Poisson approximations to nonconforming Crouzeix-Raviart approximations for both Poisson and Stokes problems in 2D.
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.