This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with dis- continuous coefficients. Our technique is based on the minimization of a least-squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method.