Abstract
A number of techniques, used as remedy to the instability of the Galerkin finite element formulation for Stokes like problems, are found in the literature. In this work we consider a coupled Stokes-Darcy problem, where in one part of the domain the fluid motion is described by Stokes equations and for the other part the fluid is in a porous medium and described by Darcy law and the conservation of mass. Such systems can be discretized by heterogeneous mixed finite elements in the two parts. A better method, from a computational point of view, consists in using a unified approach on both subdomains. Here, the coupled Stokes-Darcy problem is analyzed using equal-order velocity and pressure approximation combined with subgrid stabilization. We prove that the obtained finite element solution is stable and converges to the classical solution with optimal rates for both velocity and pressure.
Highlights
The transport of substances between surface water and groundwater has attracted a lot of interest into the coupling of viscous flows and porous media flows [1,2,3,4,5]
We prove that the obtained finite element solution is stable and converges to the classical solution with optimal rates for both velocity and pressure
In this work we consider coupled problems in fluid dynamics where the fluid in one part of the domain is described by the Stokes equations and in the other, porous media part, by the Darcy equation and mass conservation
Summary
The transport of substances between surface water and groundwater has attracted a lot of interest into the coupling of viscous flows and porous media flows [1,2,3,4,5]. In this work we consider coupled problems in fluid dynamics where the fluid in one part of the domain is described by the Stokes equations and in the other, porous media part, by the Darcy equation and mass conservation. Velocity and pressure on these two parts are mutually coupled by interface conditions derived in [6]. Such systems can be discretized by heterogeneous finite elements as analyzed by Layton et al [1]. We consider the L2-formulation of the coupled Stokes-Darcy problem as in [4], but we discretize by equal-order finite elements and use subgrid method and grad-div term to stabilize the pressure and control the natural H1(div) velocity norm on the Darcy subdomain
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
