Abstract
We provide a rigorous convergence analysis for the generalized MAC scheme on curvilinear domains proposed earlier by the authors [9]. The error analysis for the velocity field is mainly done by the energy estimate utilizing the discrete identities satisfied by the spatially compatible discretizations which properly incorporates the noslip, no-penetration condition on physical boundaries. In addition, we also proved the by Ladyzhenskaya-Babuˇska-Brezzi (LBB) condition for our scheme, which is important on its own and is essential to the pressure error estimate.