Finite-element error estimates for the MAC scheme

This paper confirms that the MAC method, applied to solve the steady-state incompressible Navier–Stokes equations, satisfies error estimates of order one. It shows that the finite-difference equations of the MAC method can be derived by combining a velocity–vorticity mixed finite-element method of degree one with an adequate quadrature formula. In the case of a rectangular grid, this interpretation simplifies the proofs of the error estimates because it allows the use of many of the tools of mathematical theory of finite-element methods. Moreover, this finite-element approach has straightforward extensions to higher-degree approximations or approximations on non-distorted meshes of three-dimensional problems.