Primal Discontinuous Galerkin Methods for Time-Dependent Coupled Surface and Subsurface Flow
Journal of Scientific Computing
Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
Journal of Computational Physics
Stokes-Darcy boundary integral solutions using preconditioners
Journal of Computational Physics
Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
SIAM Journal on Numerical Analysis
A Parallel Robin-Robin Domain Decomposition Method for the Stokes-Darcy System
SIAM Journal on Numerical Analysis
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Applied Numerical Mathematics
Spectral methods based on new formulations for coupled Stokes and Darcy equations
Journal of Computational Physics
A Decoupled Preconditioning Technique for a Mixed Stokes---Darcy Model
Journal of Scientific Computing
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In this paper we consider a coupled system made of the Stokes and Darcy equations, and we propose some iteration-by-subdomain methods based on Robin conditions on the interface. We prove the convergence of these algorithms, and for suitable finite element approximations we show that the rate of convergence is independent of the mesh size $h$. Special attention is paid to the optimization of the performance of the methods when both the kinematic viscosity $\nu$ of the fluid and the hydraulic conductivity tensor $K$ of the porous medium are very small.