  We consider the symmetric FEM-BEM coupling that connects two linear elliptic
second order partial differential equations posed in a bounded domain $\Omega$
and its complement, where the exterior problem is restated by an integral
equation on the coupling boundary $\Gamma=\partial\Omega$. We assume that the
corresponding transmission problem admits a shift theorem for data in
$H^{-1+s}$, $s \in [-1,-1+s_0]$, $s_0 > 1/2$. We analyze the discretization by
piecewise polynomials of degree $k$ for the domain variable and piecewise
polynomials of degree $k-1$ for the flux variable on the coupling boundary.
Given sufficient regularity we show that (up to logarithmic factors) the
optimal convergence $O(h^{k+1/2})$ in the $H^{-1/2}(\Gamma)$-norm is obtained
for the flux variable, while classical arguments by C\'ea-type quasi-optimality
and standard approximation results provide only $O(h^k)$ for the overall error
in the natural product norm on $H^1(\Omega)\times H^{-1/2}(\Gamma)$.
