Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
Journal of Scientific Computing
Analysis of a discontinuous finite element method for the coupled stokes and Darcy problems
Journal of Scientific Computing
Coupling Stokes and Darcy equations
Applied Numerical Mathematics
Boundary integral solutions of coupled Stokes and Darcy flows
Journal of Computational Physics
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
A strongly conservative finite element method for the coupling of Stokes and Darcy flow
Journal of Computational Physics
Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
SIAM Journal on Numerical Analysis
A Residual-Based A Posteriori Error Estimator for the Stokes-Darcy Coupled Problem
SIAM Journal on Numerical Analysis
H(div) conforming finite element methods for the coupled Stokes and Darcy problem
Journal of Computational and Applied Mathematics
Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations
Applied Numerical Mathematics
First-Order System Least Squares for Coupled Stokes-Darcy Flow
SIAM Journal on Numerical Analysis
Finite Element Approximation of Nonsolenoidal, Viscous Flows around Porous and Solid Obstacles
SIAM Journal on Numerical Analysis
A Parallel Robin-Robin Domain Decomposition Method for the Stokes-Darcy System
SIAM Journal on Numerical Analysis
New robust nonconforming finite elements of higher order
Applied Numerical Mathematics
A multilevel decoupled method for a mixed Stokes/Darcy model
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Applied Numerical Mathematics
A Mixed and Nonconforming FEM with Nonmatching Meshes for a Coupled Stokes-Darcy Model
Journal of Scientific Computing
Journal of Computational and Applied 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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The transport of substances back and forth between surface water and groundwater is a very serious problem. We study herein the mathematical model of this setting consisting of the Stokes equations in the fluid region coupled with the Darcy equations in the porous medium, coupled across the interface by the Beavers--Joseph--Saffman conditions. We prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems. This is important because there are many "legacy" codes available which have been optimized for uncoupled porous media and fluid flow.