TY - JOUR T1 - A Priori Error Estimate and Superconvergence Analysis for an Optimal Control Problem of Bilinear Type 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 -
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.