Mortar finite element discretization for the flow in a nonhomogeneous porous medium

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 8, 2007, Pages 1554-1573

  Bernardi, Christine ^a   Hecht, Frédéric ^a   Mghazli, Zoubida ^b  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b IBN TOFAIL UNIVERSITY   (Morocco)

Author keywords

Darcy's equations; Finite elements; Mortar element method; Porous media

Indexed keywords

COMPUTER SIMULATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; POROUS MATERIALS; VISCOSITY; VISCOUS FLOW;

DARCY'S EQUATIONS; INCOMPRESSIBLE FLUID; MORTAR FINITE ELEMENT DISCRETIZATION; NONHOMOGENEOUS POROUS MEDIA; VISCOUS FLUID;

INCOMPRESSIBLE FLOW;

COMPUTER SIMULATION; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; POROUS MATERIALS; VISCOSITY; VISCOUS FLOW;

EID: 33751340055     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.03.018     Document Type: Article

References (30)

1. Achdou Y., and Bernardi C. Un schéma de volumes ou éléments finis adaptatif pour les équations de Darcy à perméabilité variable. C.R. Acad. Sci. Paris 333 série I (2001) 693-698
2. Achdou Y., Bernardi C., and Coquel F. A priori and a posteriori analysis of finite volume discretizations of Darcy's equations. Numer. Math. 96 (2003) 17-42
3. Amrouche C., Bernardi C., Dauge M., and Girault V. Vector potentials in three-dimensional non smooth domains. Math. Methods Appl. Sci. 21 (1998) 823-864
4. Azaïez M., Ben Belgacem F., and Bernardi C. The mortar spectral element method in domains of operators, Part I: The divergence operator and Darcy's equations. IMA J. Numer. Anal. 26 (2006) 131-154
5. Bahouri H., Chemin J.-Y., and Gallagher I. Inégalités de Hardy précisées. C. R. Math. Acad. Sci. Paris 341 Série I (2005) 89-92
6. Ben Belgacem F. The Mortar finite element method with Lagrangian multiplier. Numer. Math. 84 (1999) 173-197
7. B. Ben Kabbour, Exploration, évaluation et protection des eaux souterraines de la Mâamora occidentale: Approche géophysique, hydrochimique, modélisation et S.I.G., Thesis, Université Ibn Tofail, Kénitra, 2002.
8. Bergam A., Bernardi C., Hecht F., and Mghazli Z. Error indicators for the mortar finite element discretization of a parabolic problem. Numer. Algorithms 34 (2003) 187-201
9. C. Bernardi, V. Girault, K.R. Rajagopal, Discretization of an unsteady flow through a porous solid modeled by Darcy's equations, in preparation.
10. Bernardi C., and Hecht F. Error indicators for the mortar finite element discretization of the Laplace equation. Math. Comput. 71 (2002) 1371-1402
11. C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: The mortar element method, in: H. Brezis, and J.-L. Lions (Eds.), Collège de France Seminar XI, Pitman, 1994, pp. 13-51.
12. Bernardi C., Maday Y., and Rapetti F. Discrétisations variationnelles de problèmes aux limites elliptiques. Collect. Math. Appl. vol. 45 (2004), Springer-Verlag
13. Bernardi C., Maday Y., and Rapetti F. Basics and some applications of the mortar element method. Gesellschaft für Angew. Math. Mech. 28 (2005) 97-123
14. Bernardi C., and Verfürth R. Adaptive finite element methods for elliptic equations with non-smooth coefficients. Numer. Math. 85 (2000) 579-608
15. In: Bourgeat A., and Kern M. (Eds). Simulation of transport around a nuclear waste disposal site: The couplex test cases. Comput. Geosci. 8 (2004) 81-215 (Special issue)
16. 1 functions. SIAM J. Numer. Anal. 41 (2003) 306-324
17. Costabel M., Dauge M., and Nicaise S. Singularities of Maxwell interface problems. Modél. Math. Anal. Numér 33 (1999) 627-649
18. Crouzeix M., and Raviart P.-A. Conforming and nonconforming finite element methods for solving the stationary Stokes equations. R.A.I.R.O. Anal. Numér. 7 R3 (1973) 33-76
19. Darcy H. Les fontaines publiques de la ville de Dijon (1856), Dalmont, Paris
20. Dauge M. Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics vol. 1341 (1988), Springer-Verlag
21. Davis T. Algorithm 832: UMFPACK - an unsymmetric-pattern multifrontal method with a column pre-ordering strategy. ACM Trans. Math. Software 30 (2004) 196-199
22. Frey P.J., and George P.-L. Maillages, applications aux éléments finis (1999), Hermès, Paris
23. Girault V., and Raviart P.-A. Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms (1986), Springer-Verlag
24. Marcinkowski L. The mortar element method with locally nonconforming elements. BIT 39 (1999) 716-739
25. de Marsily G. Quantitative Hydrology. Groundwater Hydrology for Engineers (1986), Academic Press, New York
26. p-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sci. Norm. Sup. Pisa 17 (1963) 189-206
27. Plouraboué F., Bergeron A., and Azaïez M. Generalized pressure/stream function coordinates for transport and two-phase flows in heterogeneous anisotropic porous media. Transport Porous Media 44 (2001) 281-304
28. K.R. Rajagopal, On a hierarchy of approximate models for flows of incompressible fluids through porous solids, Math. Mod. Meth. Appl. Sci., in press.
29. Verfürth R. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques (1996), Wiley & Teubner
30. Xu X., and Chen J. Multigrid for the mortar element method for the P1 nonconforming element. Numer. Math. 88 (2001) 381-398