The convergence of a family of continuous distributed mixed elliptic optimal control problems (

$$P_{\alpha }$$ ), governed by elliptic variational equalities, when the parameter $$\alpha \to \infty$$ was studied in Gariboldi - Tarzia, Appl. Math. Optim., 47 (2003), 213-230 and it has been proved that it is convergent to a distributed mixed elliptic optimal control problem ( $$P$$ ). We consider the discrete approximations ( $$P_{h\alpha }$$ ) and ( $$P_{h}$$ ) of the optimal control problems ( $$P_{\alpha }$$ ) and ( $$P$$ ) respectively, for each $$h > 0$$ and $$\alpha > 0$$ . We study the convergence of the discrete distributed optimal control problems ( $$P_{h\alpha }$$ ) and ( $$P_{h}$$ ) when $$h \to 0$$ , $$\alpha \to \infty$$ and $$(h,\alpha ) \to (0, +\infty )$$ obtaining a complete commutative diagram, including the diagonal convergence, which relates the continuous and discrete distributed mixed elliptic optimal control problems $$\left( {P_{h\alpha } } \right),\;\left( {P_{\alpha } } \right),\;\left( {P_{h} } \right)$$ and ( $$P$$ ) by taking the corresponding limits. The convergent corresponds to the optimal control, and the system and adjoint system states in adequate functional spaces.