  In this paper, we construct and analyze divergence-free finite element
methods for the Stokes problem on smooth domains. The discrete spaces are based
on the Scott-Vogelius finite element pair of arbitrary polynomial degree
greater than two. By combining the Piola transform with the classical
isoparametric framework, and with a judicious choice of degrees of freedom, we
prove that the method converges with optimal order in the energy norm. We also
show that the discrete velocity error converges with optimal order in the
$L^2$-norm. Numerical experiments are presented, which support the theoretical
results.
