  We analyze the conforming approximation of the time-harmonic Maxwell's
equations using N\'ed\'elec (edge) finite elements. We prove that the
approximation is asymptotically optimal, i.e., the approximation error in the
energy norm is bounded by the best-approximation error times a constant that
tends to one as the mesh is refined and/or the polynomial degree is increased.
Moreover, under the same conditions on the mesh and/or the polynomial degree,
we establish discrete inf-sup stability with a constant that corresponds to the
continuous constant up to a factor of two at most. Our proofs apply under
minimal regularity assumptions on the exact solution, so that general domains,
material coefficients, and right-hand sides are allowed.
