Well-posedness of a novel Lagrange multiplier formulation for fluid-poroelastic interaction

TL;DR

This paper presents a new Lagrange multiplier-based monolithic formulation for fluid-poroelastic interaction, proving its well-posedness and stability, and enabling a partitioned solution approach.

Contribution

It introduces a novel saddle point formulation with three LMs that decouples fluid and poroelastic subdomains, with proven well-posedness and stability.

Findings

Proved well-posedness of semi-discrete and fully discrete systems.

Established stability of the fully discrete formulation.

Designed a formulation enabling partitioned solution approach.

Abstract

We introduce a novel monolithic formulation that employs Lagrange multipliers (LMs) to couple a fluid flow governed by the time-dependent Stokes equations with a poroelastic structure described by the Biot equations. The formulation is developed in detail, and we establish the well-posedness of both the semi-discrete and fully discrete saddle point problems. We further prove the stability of the fully discrete system. This saddle point formulation, which utilizes three LMs, is designed to enable a partitioned approach that completely decouples the Stokes and Biot subdomains, and this approach will be explored in a subsequent work.