  The paper focuses on a new error analysis of a class of mixed FEMs for
stationary incompressible magnetohydrodynamics with the standard inf-sup stable
velocity-pressure space pairs to Navier-Stokes equations and the N\'ed\'elec's
edge element for the magnetic field. The methods have been widely used in
various numerical simulations in the last several decades, while the existing
analysis is not optimal due to the strong coupling of system and the pollution
of the lower-order N\'ed\'elec's edge approximation in analysis. In terms of a
newly modified Maxwell projection we establish new and optimal error estimates.
In particular, we prove that the method based on the commonly-used
Taylor-Hood/lowest-order N\'ed\'elec's edge element is efficient and the method
provides the second-order accuracy for numerical velocity. Two numerical
examples for the problem in both convex and nonconvex polygonal domains are
presented. Numerical results confirm our theoretical analysis.

Numerical Analysis;Numerical Analysis