TY - JOUR
T1 - Error Reduction, Convergence and Optimality for Adaptive Mixed Finite Element Methods for Diffusion Equations
AU - Shaohong Du & Xiaoping Xie
JO - Journal of Computational Mathematics
VL - 5
SP - 483
EP - 503
PY - 2012
DA - 2012/10
SN - 30
DO - http://doi.org/10.4208/jcm.1112-m3480
UR - https://global-sci.org/intro/article_detail/jcm/8445.html
KW - Adaptive mixed finite element method, Error reduction, Convergence, Quasi-optimal convergence rate.
AB - <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>