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

2014/04/11 by Kreuzer, Christian, Schedensack, Mira
#41A25 #65N12 #65N15 #65N30 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1404.3065

Abstract

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.

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• A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods
• The enriched Crouzeix-Raviart elements are equivalent to the Raviart-Thomas elements