A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE

• 来源期刊: 计算数学（英文版）
• 关键词: Bilinear control problem Finite element approximation Superconvergence A priori error estimate A posteriori error estimator
• 年，卷（期）: 2008,（4）
• 页码范围: 471-487
• 页数: 17页
• 语种: 英文

摘要

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 L2-norm error estimates and the almost optimal L8-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.