Quasioptimal cardinality of AFEM driven by nonresidual estimators

摘要

We examine adaptive finite element methods (AFEMs) with any polynomial degree satisfying rather general assumptions on the a posteriori error estimators. We show that several nonresidual estimators satisfy these assumptions. We design an AFEM with single D?rfler marking for the sum of error estimator and oscillation, prove a contraction property for the so-called total error, namely the scaled sum of energy error and oscillation, and derive quasioptimal decay rates for the total error. We also re-examine the definition and role of oscillation in the approximation class.