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

New analysis of Mixed finite element methods for incompressible Magnetohydrodynamics