Robust discontinuous Galerkin-based scheme for the fully-coupled nonlinear thermo-hydro-mechanical problem

We present and analyze a discontinuous Galerkin method for the numerical modeling of the nonlinear fully-coupled thermo-hydro-mechanic problem. We propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. We focus on the treatment of the nonlinear 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 data. A complete set of numerical simulations is presented in order to assess the convergence and robustness properties of the proposed method.