Multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity

TL;DR

This paper introduces a multirate iterative scheme combined with a multiphysics finite element method for efficiently solving fluid-saturated poroelasticity models, ensuring stability, accuracy, and reduced computational cost.

Contribution

It develops a novel multirate iterative scheme tailored for multiphysics finite element discretization of poroelasticity, with proven stability and error estimates.

Findings

The scheme is stable and conserves energy.

It maintains numerical accuracy without increased computational cost.

Numerical tests confirm theoretical stability and efficiency.

Abstract

In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics finite element method for the discretization of the space variables, and we design a multirate iterative scheme on the time scale which solve a generalized Stokes problem in the coarse time size and solve the diffusion problem in the finer time size according to the characteristics of the poroelasticity problem. Secondly, we prove that the multirate iterative scheme is stable and the numerical solution satisfies some energy conservation laws, which are important to ensure the uniqueness of solution to the decoupled computing problem. Also, we analyze the error estimates to prove that the proposed numerical method doesn't reduce the precision of numerical solution and greatly reduces the computational cost. Finally, we give the numerical tests to verify the theoretical results and draw a conclusion to summary the main results in this paper.