Mixed finite elements for second order elliptic problems in three variables
Numerische Mathematik
A relaxation procedure for domain decomposition methods using finite elements
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
On the interface boundary condition of Beavers, Joseph, and Saffman
SIAM Journal on Applied Mathematics
Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling
SIAM Journal on Numerical Analysis
Fluid-structure partitioned procedures based on Robin transmission conditions
Journal of Computational Physics
Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
SIAM Journal on Numerical Analysis
A Newton method using exact jacobians for solving fluid-structure coupling
Computers and Structures
| Hi-index | 31.45 |
The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier-Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier-Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.