Bulletin of the
Korean Mathematical Society BKMS

In this paper, we investigate the error estimates of a quadratic elliptic control problem with pointwise control constraints. The state and the co-state variables are approximated by the order $k=1$ Raviart-Thomas mixed finite element and the control variable is discretized by piecewise linear but discontinuous functions. Approximations of order $h^{\frac{3}{2}}$ in the $L^{2}$-norm and order $h$ in the $L^{\infty}$-norm for the control variable are proved.

Keywords: elliptic equations, distributed optimal control problems, $L^{\infty}$-error estimates, RT1 mixed finite element methods

MSC numbers: 49J20, 65N30