Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems

Abstract

We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three variables, i.e., the displacement, the pressure and the temperature. Lastly, we carry out numerical experiments to confirm the theoretical findings of our suggested approach.