Adaptive Finite Element Method for Optimal Control Problem Governed by Linear Quasiparabolic Integrodifferential Equations

Abstract

The mathematical formulation for a quadratic optimal control problem governed by a linear quasiparabolic integrodifferential equation is studied. The control constrains are given in an integral sense: $U_{ad}=\{u\in X;{\displaystyle \int {\mathrm{\Omega }}_{U}u⩾0,t\in [0,T]}\}$. Then the a posteriori error estimates in $L^{\infty }(0,T;H^1(\Omega ))$-norm and $L^2(0,T;L^2(\Omega ))$-norm for both the state and the control approximation are given.