Quadratic stability of flux limiters

We propose a novel approach to study the quadratic stability of 2D flux limiters for non expansive transport equations. The theory is developed constant coefficient case on cartesian grid. convergence fully discrete nonlinear scheme established in with rate not less than O (Δ x ½) norm. It way bypass Goodman–Leveque obstruction Theorem. A new corner correction proposed. formally second-order accurate away from characteristics points, satisfies maximum principle and proved be convergent tested simple numerical problems.