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Volumn 58, Issue 9, 2008, Pages 1041-1062

Hybrid and multi-point formulations of the lowest-order mixed methods for Darcy's flow on triangles

Author keywords

Brezzi Douglas Marini space; Hybrid formulations; Mixed method; Multipoint flux approximation; Raviart Thomas space

Indexed keywords

BREZZI-DOUGLAS-MARINI SPACE; HYBRID FORMULATIONS; MIXED METHOD; MULTIPOINT FLUX APPROXIMATION; RAVIART-THOMAS SPACE;

EID: 61349189650     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1785     Document Type: Article
Times cited : (29)

References (32)
  • 1
    • 0028562727 scopus 로고
    • Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities
    • Durlofsky LJ. Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities. Water Resources Research 1994; 21:965-973.
    • (1994) Water Resources Research , vol.21 , pp. 965-973
    • Durlofsky, L.J.1
  • 4
    • 61749102434 scopus 로고
    • Mixed finite element approximation of Darcy's law in porous media. Technical Report, CRS4, Cagliari, Italy
    • Bergamaschi L, Mantica S, Saleri F. Mixed finite element approximation of Darcy's law in porous media. Technical Report, CRS4, Cagliari, Italy, 1994.
    • (1994)
    • Bergamaschi, L.1    Mantica, S.2    Saleri, F.3
  • 5
    • 0028669967 scopus 로고
    • Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?
    • Mosé R, Siegel P, Ackerer P, Chavent G. Application of the mixed hybrid finite element approximation in a groundwater flow model: luxury or necessity? Water Resources Research 1994; 30:3001-3012.
    • (1994) Water Resources Research , vol.30 , pp. 3001-3012
    • Mosé, R.1    Siegel, P.2    Ackerer, P.3    Chavent, G.4
  • 6
    • 0001264684 scopus 로고    scopus 로고
    • A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements
    • Younes A, Ackerer Ph, Mosé R, Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDE with triangular elements. Journal of Computational Physics 1999; 149:148-167.
    • (1999) Journal of Computational Physics , vol.149 , pp. 148-167
    • Younes, A.1    Ackerer, P.2    Mosé, R.3    Chavent, G.4
  • 7
    • 0032776407 scopus 로고    scopus 로고
    • Modeling variable density flow and solute transport in porous medium: 1. Numerical model and verification
    • Ackerer Ph, Younes A, Mosé R. Modeling variable density flow and solute transport in porous medium: 1. Numerical model and verification. Transport in Porous Media 1999; 35:345-373.
    • (1999) Transport in Porous Media , vol.35 , pp. 345-373
    • Ackerer, P.1    Younes, A.2    Mosé, R.3
  • 8
    • 0037474431 scopus 로고    scopus 로고
    • On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles
    • Chavent G, Younes A, Ackerer Ph. On the finite volume reformulation of the mixed finite element method for elliptic and parabolic PDE on triangles. Computer Methods in Applied Mechanics and Engineering 2003; 192:655-682.
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , pp. 655-682
    • Chavent, G.1    Younes, A.2    Ackerer, P.3
  • 11
    • 61749083807 scopus 로고
    • Finite elements methods (part 1)
    • Ciarlet Lions JL eds, North-Holland: Amsterdam
    • Roberts JE, Thomas JM. Finite elements methods (part 1). In Mixed and Hybrid Methods, Ciarlet PG, Lions JL (eds), vol. II. North-Holland: Amsterdam, 1989.
    • (1989) Mixed and Hybrid Methods , vol.2
    • Roberts, J.E.1    Thomas, J.M.2
  • 12
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • Ewing RE ed, SIAM: Philadelphia, PA
    • Russel TF, Wheeler MF. Finite element and finite difference methods for continuous flows in porous media. In The Mathematics of Reservoir Simulation, Ewing RE (ed.). SIAM: Philadelphia, PA, 1983.
    • (1983) The Mathematics of Reservoir Simulation
    • Russel, T.F.1    Wheeler, M.F.2
  • 13
    • 0001669414 scopus 로고
    • On convergence of block-centered finite differences for elliptic problems
    • Weiser A, Wheeler MF. On convergence of block-centered finite differences for elliptic problems. SIAM Journal on Numerical Analysis 1988; 25:351-375.
    • (1988) SIAM Journal on Numerical Analysis , vol.25 , pp. 351-375
    • Weiser, A.1    Wheeler, M.F.2
  • 14
    • 0000381760 scopus 로고
    • Application de la théorie des éléments finis mixtes 'a l'étude d'une classe de schémas aux volumes-différences finis pour les probl'emes elliptiques
    • Baranger J, Maitre JF, Oudin F. Application de la théorie des éléments finis mixtes 'a l'étude d'une classe de schémas aux volumes-différences finis pour les probl'emes elliptiques. Comptes Rendus de l'Academie des Sciences Paris, Série 1994; 319:401-404.
    • (1994) Comptes Rendus de l'Academie des Sciences Paris, Série , vol.319 , pp. 401-404
    • Baranger, J.1    Maitre, J.F.2    Oudin, F.3
  • 15
    • 0013265698 scopus 로고
    • Mixed finite element methods as finite difference methods for solving elliptic equations on triangular elements
    • Technical Report 93-53, Department of Computational and Applied Mathematics, Rice University
    • Arbogast T, Kennan PT. Mixed finite element methods as finite difference methods for solving elliptic equations on triangular elements. Technical Report 93-53, Department of Computational and Applied Mathematics, Rice University, 1984.
    • (1984)
    • Arbogast, T.1    Kennan, P.T.2
  • 19
    • 0036924061 scopus 로고    scopus 로고
    • An introduction to multipoint flux approximations for quadrilateral grids
    • Aavatsmark I. An introduction to multipoint flux approximations for quadrilateral grids. Journal of Computational Geosciences 2002; 6:404-432.
    • (2002) Journal of Computational Geosciences , vol.6 , pp. 404-432
    • Aavatsmark, I.1
  • 20
    • 0032460761 scopus 로고    scopus 로고
    • Finite volume discretization with imposed flux continuity for the general tensor pressure equation
    • Edwards MG, Rogers CF. Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Journal of Computational Geosciences 1998; 2:259-290.
    • (1998) Journal of Computational Geosciences , vol.2 , pp. 259-290
    • Edwards, M.G.1    Rogers, C.F.2
  • 21
    • 33745319493 scopus 로고    scopus 로고
    • Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes
    • Vohralik M. Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. Mathematical Modelling and Numerical Analysis 2006; 40:367-391.
    • (2006) Mathematical Modelling and Numerical Analysis , vol.40 , pp. 367-391
    • Vohralik, M.1
  • 23
    • 33846981131 scopus 로고    scopus 로고
    • Robust convergence of multi-point flux approximations on rough grids
    • Klausen RA, Winther R. Robust convergence of multi-point flux approximations on rough grids. Numerische Mathematik 2006; 104:317-337.
    • (2006) Numerische Mathematik , vol.104 , pp. 317-337
    • Klausen, R.A.1    Winther, R.2
  • 24
    • 34248214619 scopus 로고    scopus 로고
    • A cell-centered finite difference method on quadrilaterals
    • Compatible Spatial Discretizations, Arnold DN, Bochev PB, Lehoucq RB, Nicolaides RA, Shashkov M eds, IMA Springer: New York
    • Wheeler MF, Yotov I. A cell-centered finite difference method on quadrilaterals. In Compatible Spatial Discretizations, Arnold DN, Bochev PB, Lehoucq RB, Nicolaides RA, Shashkov M (eds), IMA Vol. Ser., vol. 142. Springer: New York, 2006; 189-207.
    • (2006) Ser , vol.142 , pp. 189-207
    • Wheeler, M.F.1    Yotov, I.2
  • 26
    • 35548955728 scopus 로고    scopus 로고
    • Convergence of a symmetric MPFA method on quadrilateral grids, 05-14, Department of Mathematics, University of Pittsburgh, Pittsburgh, PA
    • Aavatsmark I, Eigestad G, Klausen RA, Wheeler MF, Yotov I. Convergence of a symmetric MPFA method on quadrilateral grids. Technical Report TR-MATH 05-14, Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 2005.
    • (2005) Technical Report TR-MATH
    • Aavatsmark, I.1    Eigestad, G.2    Klausen, R.A.3    Wheeler, M.F.4    Yotov, I.5
  • 27
    • 0002646068 scopus 로고
    • Displacement and equilibrium models in the finite element method
    • Zienkiewicz OC, Hollister G eds, New York
    • Fraeijs de Veubeke BX. Displacement and equilibrium models in the finite element method. In Stress Analysis, Zienkiewicz OC, Hollister G (eds). New York, 1965.
    • (1965) Stress Analysis
    • Fraeijs de Veubeke, B.X.1
  • 28
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • Brezzi F, Douglas Jr J, Marini LD. Two families of mixed finite elements for second order elliptic problems. Numerische Mathematik 1985; 47:217-235.
    • (1985) Numerische Mathematik , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas Jr, J.2    Marini, L.D.3
  • 30
    • 33746174150 scopus 로고    scopus 로고
    • Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equation
    • Pal M, Edwards MG, Lamb AR. Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equation. International Journal for Numerical Methods in Fluids 2006; 51:1177-1203.
    • (2006) International Journal for Numerical Methods in Fluids , vol.51 , pp. 1177-1203
    • Pal, M.1    Edwards, M.G.2    Lamb, A.R.3
  • 31
    • 21344472584 scopus 로고    scopus 로고
    • Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structures.
    • Le Potier C. Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structures. Comptes Rendu Mathematique 2005; 12:921-926.
    • (2005) Comptes Rendu Mathematique , vol.12 , pp. 921-926
    • Le Potier, C.1
  • 32
    • 0002705646 scopus 로고
    • Efficient implementation of a class of preconditioned conjugate gradient methods
    • Eisenstat SC. Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM Journal on Scientific and Statistical Computing 1981; 2:1-4.
    • (1981) SIAM Journal on Scientific and Statistical Computing , vol.2 , pp. 1-4
    • Eisenstat, S.C.1


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