Fast iterative solution of stabilised Stokes systems, part I: using simple diagonal preconditioners
SIAM Journal on Numerical Analysis
On the interface boundary condition of Beavers, Joseph, and Saffman
SIAM Journal on Applied Mathematics
A Robust Finite Element Method for Darcy--Stokes Flow
SIAM Journal on Numerical Analysis
An Efficient Method for the Navier--Stokes/Euler Coupled Equations Via a Collocation Approximation
SIAM Journal on Numerical Analysis
Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Mathematical and numerical models for coupling surface and groundwater flows
Applied Numerical Mathematics
Computing and Visualization in Science
On numerical simulation of flow through oil filters
Computing and Visualization in Science
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
A unified stabilized method for Stokes' and Darcy's equations
Journal of Computational and Applied Mathematics
Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling
SIAM Journal on Numerical Analysis
A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow
SIAM Journal on Numerical Analysis
Coupling Stokes and Darcy equations
Applied Numerical Mathematics
Coupled Generalized Nonlinear Stokes Flow with Flow through a Porous Medium
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Numerical analysis of the Navier–Stokes/Darcy coupling
Numerische Mathematik
Finite Element Approximations for Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
SIAM Journal on Numerical Analysis
Error studies of the Coupling Darcy-Stokes System with velocity-pressure formulation
Calcolo: a quarterly on numerical analysis and theory of computation
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In this paper we consider the numerical solution of the Stokes and Darcy coupled equations, which frequently appears in porous media modeling. The main contribution of this work is as follows: First, we introduce a new formulation for the Stokes/Darcy coupled equations, subject respectively to the Beavers-Joseph-Saffman interface condition and an alternative matching interface condition. Secondly, we prove the well-posedness of these weak problems by using the classical saddle point theory. Thirdly, some spectral approximations to the weak problems are proposed and analyzed, and some error estimates are provided. It is found that the new formulations significantly simplify the error analysis and numerical implementation. Finally, some two-dimensional spectral and spectral element numerical examples are provided to demonstrate the efficiency of our methods.