Error estimates of variational discretization for semilinear parabolic optimal control problems

Abstract

In this paper, variational discretization directed against the optimal control problem governed by nonlinear parabolic equations with control constraints is studied. It is known that the a priori error estimates is $|||u-u_h|||_{L^\infty(J;L^2(\Omega))}=O(h+k)$ using backward Euler method for standard finite element. In this paper, the better result $|||u-u_h|||_{L^\infty(J;L^2(\Omega))}=O(h^2+k)$ is gained. Beyond that, we get a posteriori error estimates of residual type.

Keywords

• optimal control problems
• semilinear parabolic equations
• error estimates
• finite element methods