An Efficient Iterative Decoupling Method for Thermo-Poroelasticity Based on a Four-Field Formulation

TL;DR

This paper introduces a new four-field thermo-poroelasticity model and develops both coupled and decoupled finite element methods, proving their stability and convergence without extra assumptions, supported by numerical validation.

Contribution

It presents a novel four-field formulation and an efficient iterative decoupling method with proven stability and convergence, enhancing computational approaches for thermo-poroelasticity.

Findings

Proved stability and optimal convergence of the coupled finite element method.

Established convergence of the decoupled iterative method without additional assumptions.

Numerical results confirm the effectiveness of the proposed methods.

Abstract

This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element method and a decoupled iterative finite element method. We prove the stability and optimal convergence of the coupled finite element method. Furthermore, we establish the convergence of the decoupled iterative method. This paper focuses primarily on analyzing the iterative decoupled algorithm. It demonstrates that the algorithm's convergence does not require any additional assumptions about physical parameters or stabilization parameters. Numerical results are provided to demonstrate the effectiveness and theoretical validity of these new methods.