We propose a novel approach to study the quadratic stability of 2D flux limiters for non expansive transport equations. The theory is developed for the constant coefficient case. The convergence of the fully discrete nonlinear scheme is established in 2D. It is a way to overpass the Goodman-Leveque obstruction Theorem. A new nonlinear scheme with corner correction is proposed. The scheme is formally second-order accurate away from characteristics points, satisfies the maximum principle and is proved to be convergent in quadratic norm. It is tested on simple numerical problems.