# Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity

## TL;DR

This paper introduces unconditionally stable, second-order convergent partitioned numerical methods for solving quasi-static multiple-network poroelasticity equations, enabling efficient and accurate simulations without iterative coupling.

## Contribution

The paper presents novel partitioned methods that split the equations into subproblems, achieving unconditional stability and high-order convergence without iterative coupling.

## Key findings

- Methods are unconditionally stable.
- Achieve second-order convergence in time.
- Numerical results confirm good performance.

## Abstract

In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for multiple pore networks. Two partitioned numerical methods are presented for the equations which split time discretization into solving two subequations, a Lame equation and a system of heat equations, alternatively. In contrast to the iterative coupling methods which require multiple iterations at each time step, our numerical methods solve these smaller equations only once at each time step. We prove their unconditional stability and high order convergence in time with a novel error analysis. A number of numerical results are presented to illustrate good performances of these partitioned methods.