A numerical study of primal mixed finite element approximations of Darcy equations

A numerical study of several finite element approximations for the primal mixed formulation of the Darcy equations is presented. In all cases the pressure is approximated by continuous piecewise‐linear functions. The difference between each scheme is in the choice of the finite element approximation...

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Bibliographic Details
Published in:Communications in numerical methods in engineering 2006-08, Vol.22 (8), p.901-915
Main Authors: Urquiza, J. M., N' Dri, D., Garon, A., Delfour, M. C.
Format: Article
Language:English
Subjects:
Approximation
Computational techniques
Convergence
Darcy equations
Exact sciences and technology
Finite element method
Flows through porous media
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical methods in physics
Mathematical models
mixed finite elements
Nonhomogeneous flows
Numerical analysis
Physics
primal mixed formulation
Two dimensional
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Summary:A numerical study of several finite element approximations for the primal mixed formulation of the Darcy equations is presented. In all cases the pressure is approximated by continuous piecewise‐linear functions. The difference between each scheme is in the choice of the finite element approximation space for the velocity. Numerical tests confirm the theoretical convergence of some of these schemes and we investigate the convergence properties of schemes for which theoretical results are not available. Numerical results for some 2D problems suggest that some of the new schemes provide better convergence properties for the velocity. Copyright © 2006 John Wiley & Sons, Ltd.
ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.859