Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem [article]

Paola F. Antonietti and Stefano Bonetti and Michele Botti
2022 arXiv   pre-print
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
more » ... inearized 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.
arXiv:2205.04262v3 fatcat:bas4hms7uvgy5pcq3rmlotuuwe