  We consider optimal control of an elliptic two-point boundary value problem
governed by functions of bounded variation (BV). The cost functional is
composed of a tracking term for the state and the BV-seminorm of the control.
We use the mixed formulation for the state equation together with the
variational discretization approach, where we use the classical lowest order
Raviart-Thomas finite elements for the state equation. Consequently the
variational discrete control is a piecewise constant function over the finite
element grid. We prove error estimates for the variational discretization
approach in combination with the mixed formulation of the state equation and
confirm our analytical findings with numerical experiments.
