  We present and analyze a discontinuous Galerkin method for the numerical
modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We
propose a high-order symmetric weighted interior penalty scheme that supports
general polytopal grids and is robust with respect to strong heteorgeneities in
the model coefficients. We focus on the treatment of the non-linear convective
transport term in the energy conservation equation and we propose suitable
stabilization techniques that make the scheme robust for advection-dominated
regimes. The stability analysis of the problem and the convergence of the
fixed-point linearization strategy are addressed theoretically under mild
requirements on the problem's data. A complete set of numerical simulations is
presented in order to assess the convergence and robustness properties of the
proposed method.
