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

A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems