  In this paper, we introduce a new method to study the doubly reflected
backward stochastic differential equation driven by G-Brownian motion (G-BSDE).
Our approach involves approximating the solution through a family of penalized
reflected G-BSDEs with a lower obstacle that are monotone decreasing. By
employing this approach, we establish the well-posedness of the solution of the
doubly reflected G-BSDE with the weakest known conditions, and uncover its
relationship with the fully nonlinear partial differential equation with double
obstacles for the first time.
