Convergence analysis and a novel Lagrange multiplier partitioned method for fluid-poroelastic interaction

TL;DR

This paper introduces a new partitioned numerical method for fluid-poroelastic interaction problems, using Lagrange multipliers to enforce interface conditions, with proven convergence and efficient parallel solution capabilities.

Contribution

A novel Lagrange multiplier partitioned approach for fluid-poroelastic systems that enables independent subproblem solutions and includes convergence analysis.

Findings

The method converges with proven error estimates.

Numerical experiments confirm the efficiency and accuracy of the algorithm.

The approach allows parallel computation of fluid and poroelastic subproblems.

Abstract

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish convergence of the resulting approximation. A Schur complement based algorithm is developed together with an efficient preconditioner, enabling the fluid and poroelastic structure subproblems to be decoupled and solved independently at each time step. The Lagrange multipliers approximate the interface fluxes and act as Neumann boundary conditions for the subproblems, yielding parallel solution of the Stokes and Biot equations. Numerical experiments demonstrate the effectiveness of the proposed algorithm and validate the theoretical error estimate.