@Article{JCM-30-483,
author = {Shaohong Du and Xiaoping Xie},
title = {Error Reduction, Convergence and Optimality for Adaptive Mixed Finite Element Methods for Diffusion Equations},
journal = {Journal of Computational Mathematics},
year = {2012},
volume = {30},
number = {5},
pages = {483--503},
abstract = {<p style="text-align: justify;">Error reduction, convergence and optimality are analyzed for adaptive mixed finite element methods (AMFEM) for diffusion equations without marking the oscillation of data. Firstly, the quasi-error, i.e. the sum of the stress variable error and the scaled error estimator, is shown to reduce with a fixed factor between two successive adaptive loops, up to an oscillation. Secondly, the convergence of AMFEM is obtained with respect to the quasi-error plus the divergence of the flux error. Finally, the quasi-optimal convergence rate is established for the total error, i.e. the stress variable error plus the data oscillation.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1112-m3480},
url = {http://global-sci.org/intro/article_detail/jcm/8445.html}
}