  We present a fully discrete finite element method for the interior null
controllability problem subject to the wave equation. For the numerical scheme,
piece-wise affine continuous elements in space and finite differences in time
are considered. We show that if the sharp geometric control condition holds,
our numerical scheme yields the optimal rate of convergence with respect to the
space-time mesh parameter $h$. The approach is based on the design of
stabilization terms for the discrete scheme with the goal of minimizing the
computational error.
