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http://dx.doi.org/10.4134/JKMS.2012.49.3.549

RICHARDSON EXTRAPOLATION AND DEFECT CORRECTION OF MIXED FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS  

Chen, Yanping (School of Mathematical Sciences South China Normal University)
Huang, Yunqing (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University)
Hou, Tianliang (Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.3, 2012 , pp. 549-569 More about this Journal
Abstract
In this paper asymptotic error expansions for mixed finite element approximations to a class of second order elliptic optimal control problems are derived under rectangular meshes, and the Richardson extrapolation of two different schemes and interpolation defect correction can be applied to increase the accuracy of the approximations. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators of the mixed finite element method for optimal control problems.
Keywords
optimal control problems; mixed finite element methods; asymptotic expansions; interpolation postprocessing; defect correction; a posteriori error estimators;
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