Journal Article

FINITE ELEMENT APPROXIMATIONS FOR STOKES—DARCY FLOW WITH BEAVERS—JOSEPH INTERFACE CONDITIONS

CAO, YANZHAO, ZHAO, WEIDONG, GUNZBURGER, MAX, HU, XIAOLONG, WANG, XIAOMING, HUA, FEI

2010

Overview

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. The coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. On the interface between the matrix and conduit, Beavers—Joseph interface conditions, instead of the simplified Beavers—Joseph—Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results.

• Publisher: Society for Industrial and Applied Mathematics
• Subject: Airy equation / Applied mathematics / Approximation / Aquifers / Boundary conditions / Computational fluid dynamics / Conduits / Convergence / Error analysis / Exact sciences and technology / Finite element method / Groundwater / Groundwater flow / Hydraulics / Interfaces / Karsts / Kinematics / Mathematical analysis / Mathematical models / Mathematics / Numerical analysis / Numerical analysis. Scientific computation / Numerical methods in probability and statistics / Partial differential equations / Partial differential equations, boundary value problems / Partial differential equations, initial value problems and time-dependant initial-boundary value problems / Porous materials / Sciences and techniques of general use