  We present a priori and a posteriori error analysis of a high order
hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear
elliptic problem posed on a piecewise curved, non polygonal domain. We
approximate $\Omega$ by a polygonal subdomain $\Omega_h$ and propose an HDG
discretization, which is shown to be optimal under mild assumptions related to
the non-linear source term and the distance between the boundaries of the
polygonal subdomain $\Omega_h$ and the true domain $\Omega$. Moreover, a local
non-linear post-processing of the scalar unknown is proposed and shown to
provide an additional order of convergence. A reliable and locally efficient a
posteriori error estimator that takes into account the error in the
approximation of the boundary data of $\Omega_h$ is also provided.
