A decoupled stabilized finite element method for the time–dependent Navier–Stokes/Biot problem

Abstract

In this paper, we propose a decoupled stabilized finite element method for the time-dependent Navier-Stokes/Biot problem by using the lowest equal-order finite elements. The coupling problem is divided into two subproblems which can be solved in parallel: One is the Navier-Stokes model by treating the nonlinear term explicitly, and the other is the Biot model. In the numerical scheme, we use the implicit backward Euler method in time, while treat the coupling terms explicitly. The stability analysis and error estimates are established for the proposed fully discrete scheme. Numerical results are provided to justify the theory.