scholarly journals A Fully Discretized Finite Element Approximation for an Incompressible Flow in Porous Media

2015 ◽  
Vol 3 (3) ◽  
pp. 27-43
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Incompressible Flow ◽  
Finite Element Approximation ◽  
Flow In Porous Media ◽  
Element Approximation

scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

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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