메뉴 건너뛰기




Volumn 14, Issue 2, 2010, Pages 319-341

Mixed multiscale finite element methods using approximate global information based on partial upscaling

Author keywords

Homogenization; Mixed multiscale finite elements; Porous media; Two phase flows; Upscaling

Indexed keywords

ACCURACY ASSESSMENT; COMPUTER SIMULATION; FINITE ELEMENT METHOD; FLOW MODELING; HOMOGENEITY; NUMERICAL MODEL; PERMEABILITY; POROUS MEDIUM; TWO PHASE FLOW;

EID: 77952878565     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-009-9165-7     Document Type: Article
Times cited : (19)

References (29)
  • 1
    • 81255135476 scopus 로고    scopus 로고
    • On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation
    • Aarnes, J.: On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. SIAM MMS 2, 421-439 (2004).
    • (2004) SIAM MMS , vol.2 , pp. 421-439
    • Aarnes, J.1
  • 2
    • 55149114207 scopus 로고    scopus 로고
    • Mixed multiscale finite element methods using limited global information
    • Aarnes, J., Efendiev, Y., Jiang, L.: Mixed multiscale finite element methods using limited global information. SIAM Multiscale Model. Simul. 7(2), 655-676 (2008).
    • (2008) SIAM Multiscale Model. Simul. , vol.7 , Issue.2 , pp. 655-676
    • Aarnes, J.1    Efendiev, Y.2    Jiang, L.3
  • 3
    • 34249074153 scopus 로고    scopus 로고
    • A hierarchical multiscale method for two-phase flow based on upon mixed finite elements and nonuniform coarse grids
    • Aarnes, J., Krogstad, S., Lie, K. A.: A hierarchical multiscale method for two-phase flow based on upon mixed finite elements and nonuniform coarse grids. Multiscale Model. Simul. 5(2), 337-363 (2006).
    • (2006) Multiscale Model. Simul. , vol.5 , Issue.2 , pp. 337-363
    • Aarnes, J.1    Krogstad, S.2    Lie, K.A.3
  • 4
    • 34548322704 scopus 로고    scopus 로고
    • Coarsening of three-dimensional structured and unstructured grids for subsurface flow
    • Aarnes, J. E., Hauge, V., Efendiev, Y.: Coarsening of three-dimensional structured and unstructured grids for subsurface flow. Adv. Water Resour. 30(11), 2177-2193 (2007).
    • (2007) Adv. Water Resour. , vol.30 , Issue.11 , pp. 2177-2193
    • Aarnes, J.E.1    Hauge, V.2    Efendiev, Y.3
  • 5
    • 33748438382 scopus 로고    scopus 로고
    • A multiscale finite element method for numerical homogenization
    • Allaire, G., Brizzi, R.: A multiscale finite element method for numerical homogenization. SIAM MMS 4(3), 790-812 (2005).
    • (2005) SIAM MMS , vol.4 , Issue.3 , pp. 790-812
    • Allaire, G.1    Brizzi, R.2
  • 6
    • 0036927305 scopus 로고    scopus 로고
    • Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow
    • Arbogast, T.: Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow. Comput. Geosci. 6, 453-481 (2002).
    • (2002) Comput. Geosci. , vol.6 , pp. 453-481
    • Arbogast, T.1
  • 7
    • 84990602687 scopus 로고
    • Compactness method in the theory of homogenization
    • Avellaneda, M., Lin, F.-H.: Compactness method in the theory of homogenization. Commun. Pure Appl. Math. 40(6), 803-847 (1987).
    • (1987) Commun. Pure Appl. Math. , vol.40 , Issue.6 , pp. 803-847
    • Avellaneda, M.1    Lin, F.-H.2
  • 8
    • 0000828256 scopus 로고
    • Generalized finite element methods: Their performance and their relation to mixed methods
    • Babuška, I., Osborn, E.: Generalized finite element methods: their performance and their relation to mixed methods. SIAM J. Numer. Anal. 20, 510-536 (1983).
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 510-536
    • Babuška, I.1    Osborn, E.2
  • 9
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • Babuška, I., Caloz, G., Osborn, E.: Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31, 945-981 (1994).
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 945-981
    • Babuška, I.1    Caloz, G.2    Osborn, E.3
  • 10
    • 0003332875 scopus 로고    scopus 로고
    • Interacting with the subgrid world
    • Boca Raton, FL: Chapman & Hall/CRC
    • Brezzi, F.: Interacting with the subgrid world. In: Numerical Analysis 1999 (Dundee), pp. 69-82. Chapman & Hall/CRC, Boca Raton, FL (2000).
    • (2000) Numerical Analysis 1999 (Dundee) , pp. 69-82
    • Brezzi, F.1
  • 12
    • 0037376524 scopus 로고    scopus 로고
    • A mixed multiscale finite element method for elliptic problems with oscillating coefficients
    • Chen, Z., Hou, T. Y.: A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comput. 72, 541-576 (2002).
    • (2002) Math. Comput. , vol.72 , pp. 541-576
    • Chen, Z.1    Hou, T.Y.2
  • 13
    • 0141539144 scopus 로고    scopus 로고
    • A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations
    • Chen, Y., Durlofsky, L. J., Gerritsen, M., Wen, X. H.: A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour. 26, 1041-1060 (2003).
    • (2003) Adv. Water Resour. , vol.26 , pp. 1041-1060
    • Chen, Y.1    Durlofsky, L.J.2    Gerritsen, M.3    Wen, X.H.4
  • 14
    • 2942612789 scopus 로고    scopus 로고
    • Tenth SPE comparative solution project: A comparison of upscaling techniques
    • Christie, M., Blunt, M.: Tenth SPE comparative solution project: a comparison of upscaling techniques. SPE Reserv. Evalu. Eng. 4, 308-317 (2001).
    • (2001) SPE Reserv. Evalu. Eng. , vol.4 , pp. 308-317
    • Christie, M.1    Blunt, M.2
  • 16
    • 84944838250 scopus 로고
    • Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media
    • Durlofsky, L. J.: Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res. 27, 699-708 (1991).
    • (1991) Water Resour. Res. , vol.27 , pp. 699-708
    • Durlofsky, L.J.1
  • 17
    • 33846388935 scopus 로고    scopus 로고
    • An adaptive local-global multiscale finite volume element method for two-phase flow simulations
    • Durlofsky, L. J., Efendiev, Y., Ginting, V.: An adaptive local-global multiscale finite volume element method for two-phase flow simulations. Adv. Water Resour. 30, 576-588 (2007).
    • (2007) Adv. Water Resour. , vol.30 , pp. 576-588
    • Durlofsky, L.J.1    Efendiev, Y.2    Ginting, V.3
  • 18
    • 85128810254 scopus 로고    scopus 로고
    • Multiscale finite element methods for nonlinear problems and their applications
    • Efendiev, Y., Hou, T., Ginting, V.: Multiscale finite element methods for nonlinear problems and their applications. Commun. Math. Sci. 2, 553-589 (2004).
    • (2004) Commun. Math. Sci. , vol.2 , pp. 553-589
    • Efendiev, Y.1    Hou, T.2    Ginting, V.3
  • 19
    • 33751252248 scopus 로고    scopus 로고
    • Accurate multiscale finite element methods for two-phase flow simulations
    • Efendiev, Y., Ginting, V., Hou, T., Ewing, R.: Accurate multiscale finite element methods for two-phase flow simulations. J. Comput. Phys. 220(1), 155-174 (2006).
    • (2006) J. Comput. Phys. , vol.220 , Issue.1 , pp. 155-174
    • Efendiev, Y.1    Ginting, V.2    Hou, T.3    Ewing, R.4
  • 21
    • 18144399279 scopus 로고    scopus 로고
    • Towards multiscale functions: Enriching finite element spaces with local but not bubble-like functions
    • Franca, L., Madureira, A., Valentin, F.: Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions. Comput. Methods Appl. Mech. Eng. 194(27-29), 3006-3021 (2005).
    • (2005) Comput. Methods Appl. Mech. Eng. , vol.194 , Issue.27-29 , pp. 3006-3021
    • Franca, L.1    Madureira, A.2    Valentin, F.3
  • 22
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou, T. Y., Wu, X. H.: A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134, 169-189 (1997).
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.H.2
  • 23
  • 25
    • 33747491187 scopus 로고    scopus 로고
    • First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
    • Moskow, S., Vogelius, M.: First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof. Proc. R. Soc. Edinb. Sect. A 127(6), 1263-1299 (1997).
    • (1997) Proc. R. Soc. Edinb. Sect. A , vol.127 , Issue.6 , pp. 1263-1299
    • Moskow, S.1    Vogelius, M.2
  • 26
    • 0002615068 scopus 로고    scopus 로고
    • H-convergence, in topics in the mathematical modeling of composite materials
    • A. Cherkaev and R. V. Kohn (Eds.), Boston: Birkhauser
    • Murat, F., Tartar, L.: H-convergence, in topics in the mathematical modeling of composite materials. In: Cherkaev, A., Kohn, R. V. (eds.) Progress in Nonlinear Differential Equations and their Applications. Birkhauser, Boston (1997).
    • (1997) Progress in Nonlinear Differential Equations and Their Applications
    • Murat, F.1    Tartar, L.2
  • 28
    • 3042732038 scopus 로고    scopus 로고
    • Capturing small scales in elliptic problems using a residual-free bubbles finite element method
    • (electronic)
    • Sangalli, G.: Capturing small scales in elliptic problems using a residual-free bubbles finite element method. Multiscale Model. Simul. 1, 485-503 (2003) (electronic).
    • (2003) Multiscale Model. Simul. , vol.1 , pp. 485-503
    • Sangalli, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.