메뉴 건너뛰기




Volumn 59, Issue 3, 2004, Pages 365-388

From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensions

Author keywords

Elliptic problem; Finite volume method; Mixed finite element method

Indexed keywords

FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FLUXES; TENSORS;

EID: 1442340218     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.874     Document Type: Article
Times cited : (55)

References (37)
  • 1
    • 0033617511 scopus 로고    scopus 로고
    • Numerical methods for reactive transport on rectangular and streamline oriented grids
    • Cirpka O, Frind E. Helmig R. Numerical methods for reactive transport on rectangular and streamline oriented grids. Advances in Water Resources 1999; 22(7):711-728.
    • (1999) Advances in Water Resources , vol.22 , Issue.7 , pp. 711-728
    • Cirpka, O.1    Frind, E.2    Helmig, R.3
  • 2
    • 0002478314 scopus 로고    scopus 로고
    • M-Matrix flux splitting for general full tensor discretization operators on structured and unstructured grids
    • Edwards M. M-Matrix flux splitting for general full tensor discretization operators on structured and unstructured grids. Journal of Computational Physics 2000; 160:1-28.
    • (2000) Journal of Computational Physics , vol.160 , pp. 1-28
    • Edwards, M.1
  • 3
    • 0036923067 scopus 로고    scopus 로고
    • Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids
    • Edwards M. Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids. Computational Geosciences 2002; 6:433-452.
    • (2002) Computational Geosciences , vol.6 , pp. 433-452
    • Edwards, M.1
  • 4
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Lectures Notes in Mathematics, Springer: New York
    • Raviart PA, Thomas JM. A mixed finite element method for second order elliptic problems. Mathematical Aspects of the Finite Element Method, Lectures Notes in Mathematics, vol. 606. Springer: New York, 1977; 292-315.
    • (1977) Mathematical Aspects of the Finite Element Method , vol.606 , pp. 292-315
    • Raviart, P.A.1    Thomas, J.M.2
  • 8
    • 0036704708 scopus 로고    scopus 로고
    • Computational engineering and science methodologies for modeling and simulation of subsurface applications
    • Wheeler MF, Peszynska M. Computational engineering and science methodologies for modeling and simulation of subsurface applications. Advances in Water Resources 2002; 25:1147-1173.
    • (2002) Advances in Water Resources , vol.25 , pp. 1147-1173
    • Wheeler, M.F.1    Peszynska, M.2
  • 10
    • 0028669967 scopus 로고
    • Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity?
    • Mose R, Siegel P, Ackerer Ph, Chavent G. Application of the mixed hybrid finite element approximation in a groundwater flow model: luxury or necessity? Water Resources Research 1994; 30(11):3001-3012.
    • (1994) Water Resources Research , vol.30 , Issue.11 , pp. 3001-3012
    • Mose, R.1    Siegel, P.2    Ackerer, P.3    Chavent, G.4
  • 11
    • 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: 30(4):965-973.
    • (1994) Water Resources Research , vol.30 , Issue.4 , pp. 965-973
    • Durlofsky, L.J.1
  • 12
    • 0029527594 scopus 로고
    • Mixed finite elements for accurate particle tracking in saturated groundwater flow
    • Kaasschieter EF. Mixed finite elements for accurate particle tracking in saturated groundwater flow. Advances in Water Resources 1995; 18(5):277-294.
    • (1995) Advances in Water Resources , vol.18 , Issue.5 , pp. 277-294
    • Kaasschieter, E.F.1
  • 13
    • 0025538951 scopus 로고
    • New mixed finite element schemes for current continuity equations
    • Marini LD, Pietra P. New mixed finite element schemes for current continuity equations. COMPEL 1990; 9(4):257-268.
    • (1990) COMPEL , vol.9 , Issue.4 , pp. 257-268
    • Marini, L.D.1    Pietra, P.2
  • 16
  • 17
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • Ewing RE (eds). SIAM: Philadelphia
    • Russel TF, Wheeler MF. Finite element and finite difference methods for continuous flows in porous media. In Mathematics of Reservoir Simulation. Ewing RE (eds). SIAM: Philadelphia. 1983.
    • (1983) Mathematics of Reservoir Simulation
    • Russel, T.F.1    Wheeler, M.F.2
  • 18
    • 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
  • 19
    • 0026398228 scopus 로고
    • A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems
    • Chavent G, Roberts J. A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems. Advances in Water Resources 1991; 14:329-348.
    • (1991) Advances in Water Resources , vol.14 , pp. 329-348
    • Chavent, G.1    Roberts, J.2
  • 20
    • 0000381760 scopus 로고
    • Application de la théorie des éléments finis mixtes à l'étude d'une classe de schémas aux volumes-différences firis pour les problèmes elliptiques
    • Paris
    • Baranger J, Maitre JF, Oudin F. Application de la théorie des éléments finis mixtes à l'étude d'une classe de schémas aux volumes-différences firis pour les problèmes elliptiques. Comptes Rendus de l'Académie des Sciences. Paris 1994; 319(1):401-404.
    • (1994) Comptes Rendus de L'Académie des Sciences , vol.319 , Issue.1 , pp. 401-404
    • Baranger, J.1    Maitre, J.F.2    Oudin, F.3
  • 21
    • 0000060649 scopus 로고    scopus 로고
    • Comment on "Application of the mixed hybrid finite approximation in a groundwater flow model: Luxury or necessity?" by Mose et al
    • Cordes C, Kinzelbach W. Comment on "Application of the mixed hybrid finite approximation in a groundwater flow model: luxury or necessity?" by Mose et al. Water Resources Research 1996; 32(6):1905-1909.
    • (1996) Water Resources Research , vol.32 , Issue.6 , pp. 1905-1909
    • Cordes, C.1    Kinzelbach, W.2
  • 23
    • 0005534014 scopus 로고    scopus 로고
    • Reply to the Comment on 'Application of the mixed hybrid finite approximation in a groundwater flow model: Luxury or necessity?' by Mose et al
    • Ackerer Ph, Mose R, Siegel P. Reply to the Comment on 'Application of the mixed hybrid finite approximation in a groundwater flow model: luxury or necessity?' by Mose et al. Water Resources Research 1996; 32(6): 1911-1913.
    • (1996) Water Resources Research , vol.32 , Issue.6 , pp. 1911-1913
    • Ackerer, Ph.1    Mose, R.2    Siegel, P.3
  • 24
    • 0002799707 scopus 로고    scopus 로고
    • Triangular mixed finite elements versus finite differences and finite volumes in groundwater flow modeling
    • Cancun, Mexico, Computational Mechanics Publications
    • Cordes C, Putti M. Triangular mixed finite elements versus finite differences and finite volumes in groundwater flow modeling. Proceedings of the Computational Methods in Subsurface Flow and Transport Problems, Cancun. Mexico, Computational Mechanics Publications. 1996: 61-69.
    • (1996) Proceedings of the Computational Methods in Subsurface Flow and Transport Problems , pp. 61-69
    • Cordes, C.1    Putti, M.2
  • 26
    • 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, Mose 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    Mose, R.3    Chavent, G.4
  • 27
    • 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
  • 28
    • 0036924076 scopus 로고    scopus 로고
    • A finite-volume method with hexahedral multiblock grids for modeling flow in porous media
    • Lee SH, Jenny P, Tchelepi HA. A finite-volume method with hexahedral multiblock grids for modeling flow in porous media. Computational Geosciences 2002; 6:353-379.
    • (2002) Computational Geosciences , vol.6 , pp. 353-379
    • Lee, S.H.1    Jenny, P.2    Tchelepi, H.A.3
  • 29
    • 0001296955 scopus 로고    scopus 로고
    • Cordes. Finite element approximation of the diffusion operator on tetrahedra
    • Putti M, Cordes. Finite element approximation of the diffusion operator on tetrahedra. SIAM Journal on Scientific Computing 1998; 19(4):1154-1168.
    • (1998) SIAM Journal on Scientific Computing , vol.19 , Issue.4 , pp. 1154-1168
    • Putti, M.1
  • 30
    • 0001198473 scopus 로고    scopus 로고
    • Mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences
    • Arbogast T, Wheeler MF, Yotov I. Mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences. SIAM Journal on Numerical Analysis 1997; 34(2):828-852.
    • (1997) SIAM Journal on Numerical Analysis , vol.34 , Issue.2 , pp. 828-852
    • Arbogast, T.1    Wheeler, M.F.2    Yotov, I.3
  • 31
    • 0026747450 scopus 로고
    • Three dimensional bioremediation modeling in heterogeneous porous media
    • Russell TF, Ewing RE, Brebbia CA, Gray WG. Pindar GF (eds), Computational Mechanics Publications: Southampton, U.K
    • Wheeler MF, Roberson KR, Chilakapati A. Three dimensional bioremediation modeling in heterogeneous porous media. In Computational Methods in Water Resources IX, Mathematical, Modeling in Water Resources, Russell TF, Ewing RE, Brebbia CA, Gray WG. Pindar GF (eds), vol. 2. Computational Mechanics Publications: Southampton, U.K., 1992; 299-315.
    • (1992) Computational Methods in Water Resources IX, Mathematical, Modeling in Water Resources , vol.2 , pp. 299-315
    • Wheeler, M.F.1    Roberson, K.R.2    Chilakapati, A.3
  • 33
    • 84944838250 scopus 로고
    • Numerical calculation of equivalent grid block permeability tensors for heterogeneous media
    • Durlofsky LJ. Numerical calculation of equivalent grid block permeability tensors for heterogeneous media. Water Resources Research 1991; 17(5):699-708.
    • (1991) Water Resources Research , vol.17 , Issue.5 , pp. 699-708
    • Durlofsky, L.J.1
  • 34
    • 0002705646 scopus 로고
    • Efficient implementation of a class of preconditioned conjugate gradient methods
    • Eisenstat S. 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.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.