A coupling of Galerkin and mixed finite element methods for the quasi-static thermo-poroelasticity with nonlinear convective transport

In this paper, we propose a combined Galerkin and mixed finite element methods to analyze the fully coupled nonlinear thermo-poroelastic model problems. We design the Galerkin element method for the temperature, the mixed finite element method for the pressure, Galerkin finite element method for the elastic displacement. We linearize the nonlinear convec-tive transport term in the energy balance equation and establish the fully discrete finite element schemes. The stability and convergence of the coupled method are obtained. In particular, previous works have required certain time step restrictions, but we unconditionally prove optimal error estimates without certain extra restrictions on both time step and spatial meshes. Finally, some numerical examples are presented to illustrate the accuracy of the method confirm the unconditional stability of the method.

Automated summary

A combined Galerkin and mixed finite element method is proposed to analyze fully coupled nonlinear thermo-poroelastic model problems. The method utilizes Galerkin finite element method for temperature, mixed finite element method for pressure, and Galerkin finite element method for elastic displacement. The stability and convergence of the method are obtained, and optimal error estimates are proved without certain extra restrictions on both time step and spatial meshes.