  A theoretical analysis of the finite element method for a generalized Robin
boundary value problem, which involves a second-order differential operator on
the boundary, is presented. If $\Omega$ is a general smooth domain with a
curved boundary, we need to introduce an approximate domain $\Omega_h$ and to
address issues owing to the domain perturbation $\Omega \neq \Omega_h$. In
contrast to the transformation approach used in existing studies, we employ the
extension approach, which is easier to handle in practical computation, in
order to construct a numerical scheme. Assuming that approximate domains and
function spaces are given by isoparametric finite elements of order $k$, we
prove the optimal rate of convergence in the $H^1$- and $L^2$-norms. A
numerical example is given for the piecewise linear case $k = 1$.
