  In this paper, we carry out the error analysis for the structure-preserving
discretization of the incompressible MHD system. This system, as a coupled
system of Navier-Stokes equations and Maxwell's equations, is nonlinear. We use
its energy estimate and the underlying physical structure to facilitate the
error analysis. Under certain CFL conditions, we prove the optimal order of
convergence. To support the theoretical results, we also present numerical
tests.
