ELLIPTIC RECONSTRUCTION AND A POSTERIORI ERROR ESTIMATES FOR FULLY DISCRETE SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS

作     者：Ram Manohar Rajen Kumar Sinha Ram Manohar;Rajen Kumar Sinha

作者机构：Department of MathematicsIndian Institute of Technology GuwahatiGuwahati-781039India 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2022年第40卷第2期

页      面：147-176页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Semilinear parabolic optimal control problem Finite element method The backward Euler method Elliptic reconstruction A posteriori error estimates 

摘      要：This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems.Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto[25],a residual based a posteriori error estimators for the state,co-state and control variables are derived.The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements,whereas the piecewise constant functions are employed for the control variable.The temporal discretization is based on the backward Euler method.We derive a posteriori error estimates for the state,co-state and control variables in the L^(∞)(0,T;L^(2)(Ω))-norm.Finally,a numerical experiment is performed to illustrate the performance of the derived estimators.