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

TL;DR

This paper develops and analyzes a coupled finite element method for simulating wave propagation in thermo-poroelastic materials, ensuring stability and accuracy in the frequency domain with proven error estimates.

Contribution

It introduces a stabilized coupling of conforming and mixed finite element spaces for thermo-poroelasticity, addressing volumetric locking and oscillations, with rigorous theoretical analysis and validation.

Findings

Method is stable and free of volumetric locking.

Achieves optimal error estimates for all variables.

Numerical results confirm accuracy and robustness.

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.