Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
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
Locally Conservative Coupling of Stokes and Darcy Flows
SIAM Journal on Numerical Analysis
Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
Journal of Scientific Computing
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
SIAM Journal on Numerical Analysis
Characterizing the inf-sup condition on product spaces
Numerische Mathematik
Coupled Generalized Nonlinear Stokes Flow with Flow through a Porous Medium
SIAM Journal on Numerical Analysis
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We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.