TY - JOUR
T1 - A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type
AU - Danping Yang, Yanzhen Chang & Wenbin Liu
JO - Journal of Computational Mathematics
VL - 4
SP - 471
EP - 487
PY - 2008
DA - 2008/08
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8638.html
KW - Bilinear control problem, Finite element approximation, Superconvergence, A priori error estimate, A posteriori error estimator.
AB - <p style="text-align: justify;">In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal $L^2$-norm error estimates and the almost optimal $L^\infty$-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.</p>