TY - JOUR
T1 - Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems
AU - Tang Liu, Ningning Yan & Shuhua Zhang
JO - Journal of Computational Mathematics
VL - 1
SP - 55
EP - 71
PY - 2010
DA - 2010/02
SN - 28
DO - http://doi.org/10.4208/jcm.2009.09-m1001
UR - https://global-sci.org/intro/article_detail/jcm/8507.html
KW - Optimal control problem, Finite element methods, Asymptotic error expansions, Defect correction, A posteriori error estimates.
AB - <p style="text-align: justify;">Asymptotic error expansions in $H^1$-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectangular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation. &nbsp;</p>