TY - JOUR
T1 - Global Superconvergence for Optimal Control Problems Governed by Stokes Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 283
EP - 302
PY - 2006
DA - 2006/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/901.html
KW - optimal control, Stokes equations, finite element approximation, global superconvergence, recovery, a posteriori error estimate.
AB - <p style="text-align: justify;">In this paper, the global superconvergence analysis for the
finite element approximation of the distributed optimal control governed
by Stokes equations is discussed. For the control, a global
superconvergence result is derived by applying patch recovery technique.
For the state and the co-state, the global superconvergence results are
derived by applying some postprocessing techniques for the
bilinear-constant scheme over the uniform rectangular meshes. Based on
the global superconvergence analysis, recovery type a posteriori error
estimates are derived. It is shown that the recovery type a posteriori
error estimators provided in this paper are asymptotically exact if the
conditions for the superconvergence are satisfied.</p>