Discontinuous Galerkin Approximation of the Fully Coupled Thermo-poroelastic Problem

Abstract

We present and analyze a discontinuous Galerkin method for the numerical modeling of the nonlinear fully coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal and polyhedral grids based on a novel four-field formulation of the problem. To handle the nonlinear convective transport term in the energy conservation equation we adopt a fixed-point linearization strategy. We perform a robust stability analysis for the linearized semidiscrete problem under mild requirements on the problem’s physical parameters. A priori hp-version error estimates in suitable energy norms are also derived. A complete set of numerical simulations is presented in order to validate the theoretical analysis, to inspect numerically the robustness properties, and to test the capability of the proposed method in a practical scenario inspired by a geothermal problem.