Optimal control problems in elliptic equations have been used for parameter identification and data assimilation, with applications in biomedicine, seismology, structural design, and other fields. The first-discretize-then-optimize (FDTO) strategy has become more popular due to the complexity of elliptic equations, the complexity of the models and special constraints for the control, and the improved performance of optimization algorithms. Several of these algorithms take adavantage of automatic differentiation tools, thus eliminating the need to compute adjoint states. However, since solving the state equation is necessary in each iteration of the optimization algorithm, its complexity can slow down every iteration. In contrast, the first-optimize-then-discretize (FOTD) strategy is based on reducing the state equations, adjoints, and the first-order optimality condition to a coupled discrete problem. Although this new problem is much more complex than the discrete states equation, since the coupled system can be non-linear even if the states equation is linear, it only needs to be solved once. It is also possible to take advantage of robust algorithms for solving nonlinear equations. This talk will present examples of using FEniCS with the multiphenics package to implement the FOTD strategy in optimal control problems. In particular, synthetic experiments will be shown for coseismic jump recovery in subduction earthquakes and the detection of obstacles immersed in fluids by identifying a permeability term with adaptive refinement.