Mimetic discretizations of elliptic control problems (Q1955932)

The authors consider the following optimal control problem \[ \min_{u\in K} \Biggl\{{1\over 2}\Biggl\| y-\overline y\Biggr\|^2_{L^2(\Omega)}+ {1\over 2}\Biggl\| F-\overline F\Biggr\|^2_{L^2(\Omega)}+ {\alpha\over 2}\Biggl\| u-\overline u\Biggr\|^2_{L^2(\Omega)}\Biggr\}, \] \[ \begin{aligned} F=-\nabla y\quad &\text{in }\Omega,\\ \text{div}(F)= f+ u\quad &\text{in }\Omega,\\ y= 0\quad &\text{on }\delta\Omega.\end{aligned} \] Low- and high-order mimetic discretizations are considered and a priori error estimates are derived. -- Numerical experiments are given.