Analysis and finite element approximation of a coupled, continuum pipe-flow/Darcy model for flow in porous media with embedded conduits

2010 ◽  
Vol 27 (5) ◽  
pp. 1242-1252 ◽  
Author(s):  
Yanzhao Cao ◽  
Max Gunzburger ◽  
Fei Hua ◽  
Xiaoming Wang
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Pipe Flow ◽  
Finite Element Approximation ◽  
Flow In Porous Media ◽  
Element Approximation ◽  
Darcy Model

scholarly journals ANISOTROPIC QUASI-WILSON ELEMENT WITH CONFORMING FINITE ELEMENT APPROXIMATION FOR COUPLED CONTINUUM PIPE-FLOW/DARCY MODEL IN KARST AQUIFERS

2016 ◽  
Vol 21 (4) ◽  
pp. 431-449 ◽  
Author(s):  
Wei Liu ◽  
Jintao Cui
Keyword(s):  
Finite Element ◽  
Pipe Flow ◽  
Finite Element Approximation ◽  
Flow In Porous Media ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Approximation Solution ◽  
Darcy Model ◽  
Conforming Finite Element ◽  
Wilson Element

This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in both L2 and H1 norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme.

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