Korean J. Math.  Vol 22, No 3 (2014)  pp.429-441
DOI: https://doi.org/10.11568/kjm.2014.22.3.429

Hierarchical error estimators for lowest-order mixed finite element methods

Kwang-Yeon Kim


In this work we study two a posteriori error estimators of hierarchical type for lowest-order mixed finite element methods.One estimator is computed by solving a global defect problem based on the splitting of the lowest-order Brezzi--Douglas--Marini space, and the other estimator is locally computable by applying the standard localization to the first estimator. We establish the reliability and efficiency of both estimators by comparing them with the standard residual estimator. In addition, it is shown that the error estimator based on the global defect problem is asymptotically exact under suitable conditions.


a posteriori error estimation, mixed finite element method, hierarchical error estimator, asymptotic exactness

Subject classification

65N30, 65N15


This study was supported by 2013 Research Grant from Kangwon National Uni- versity (No. C1009911-01-01).

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