Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem
Abstract
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear 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 non-linear convective transport term in the energy conservation equation we adopt a fixed-point linearization strategy. We perform a robust stability analysis for the linearized semi-discrete problem under mild requirements on the problem data. 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.
Keywords
Cite
@article{arxiv.2205.04262,
title = {Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem},
author = {Paola F. Antonietti and Stefano Bonetti and Michele Botti},
journal= {arXiv preprint arXiv:2205.04262},
year = {2022}
}