Coupling of conforming and mixed finite element methods for a model of wave propagation in thermo-poroelasticity in the frequency domain

Abstract

A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency domain. The variational formulation is analyzed within the framework of Fredholm's alternative and T-coercivity. Under appropriate assumptions on the coefficients, the well-posedness of the problem is proved. For its discretization, we propose a stabilized coupling of conforming and mixed finite element spaces, which are free of volumetric locking, and both, pressure as well as temperature oscillations. By incorporating projections in certain sesquilinear forms, the well-posedness of the finite element solution can be obtained through a similar reasoning as in the continuous case. Optimal error estimates are derived for all variables. Numerical studies validate the accuracy and robustness of the proposed method.