메뉴 건너뛰기




Volumn 218, Issue 2, 2006, Pages 654-676

A stochastic variational multiscale method for diffusion in heterogeneous random media

Author keywords

Generalized polynomial chaos; Multiscale finite element; Operator upscaling; Stochastic diffusion; Subgrid modelling; Variational multiscale

Indexed keywords

FINITE ELEMENT METHOD; NUMERICAL METHODS; POLYNOMIALS; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

EID: 33748882856     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.02.026     Document Type: Article
Times cited : (51)

References (49)
  • 1
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou T.Y., and Wu X.H. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169-189
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.H.2
  • 2
    • 0004025336 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • Milton G. Theory of Composites (2002), Cambridge University Press, Cambridge, UK
    • (2002) Theory of Composites
    • Milton, G.1
  • 3
    • 18444389215 scopus 로고    scopus 로고
    • Analysis of a two-scale, locally conservative subgrid upscaling for elliptic problems
    • Arbogast T. Analysis of a two-scale, locally conservative subgrid upscaling for elliptic problems. SIAM J. Numer. Anal. 42 (2004) 576-598
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 576-598
    • Arbogast, T.1
  • 4
    • 0036962026 scopus 로고    scopus 로고
    • A two-scale numerical subgrid technique for waterflood simulations
    • Arbogast T., and Bryant S.L. A two-scale numerical subgrid technique for waterflood simulations. SPE J. (2002) 446-457
    • (2002) SPE J. , pp. 446-457
    • Arbogast, T.1    Bryant, S.L.2
  • 5
    • 0031260069 scopus 로고    scopus 로고
    • Calculating equivalent permeability: a review
    • Renard P., and de Marsily G. Calculating equivalent permeability: a review. Adv. Water Res. 20 (1997) 253-278
    • (1997) Adv. Water Res. , vol.20 , pp. 253-278
    • Renard, P.1    de Marsily, G.2
  • 6
    • 0031674480 scopus 로고    scopus 로고
    • An operator-based approach to upscaling the pressure equation
    • Computational Methods in Water Resources XII, Computational Mechanics Publications, Southampton, UK
    • Arbogast T., Minkoff S.E., and Keenan P.T. An operator-based approach to upscaling the pressure equation. Computational Methods in Water Resources XII. Computational Methods in Contamination and Remediation of Water Resources Vol. 1 (1998), Computational Mechanics Publications, Southampton, UK
    • (1998) Computational Methods in Contamination and Remediation of Water Resources , vol.1
    • Arbogast, T.1    Minkoff, S.E.2    Keenan, P.T.3
  • 7
    • 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 (2002) 453-480
    • (2002) Comput. Geosci. , vol.6 , pp. 453-480
    • Arbogast, T.1
  • 8
    • 0002596717 scopus 로고    scopus 로고
    • Numerical subgrid upscaling of two-phase flow in porous media
    • Springer, Berlin
    • Arbogast T. Numerical subgrid upscaling of two-phase flow in porous media. Lecture Notes in Physics vol. 552 (2000), Springer, Berlin
    • (2000) Lecture Notes in Physics , vol.552
    • Arbogast, T.1
  • 9
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multi-scale methods
    • Engquist W.E.B. The heterogeneous multi-scale methods. Comm. Math. Sci. 1 1 (2003) 87-133
    • (2003) Comm. Math. Sci. , vol.1 , Issue.1 , pp. 87-133
    • Engquist, W.E.B.1
  • 10
    • 85190764391 scopus 로고    scopus 로고
    • W.E.P.B. Ming, P.W. Zhang, Analysis of the heterogeneous multiscale method for elliptic homogenization problems, preprint, 2003.
  • 11
    • 0039982148 scopus 로고    scopus 로고
    • Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
    • Hou T.Y., Wu X.H., and Cai Z.Q. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comput. 68 (1999) 913-943
    • (1999) Math. Comput. , vol.68 , pp. 913-943
    • Hou, T.Y.1    Wu, X.H.2    Cai, Z.Q.3
  • 12
    • 33748886945 scopus 로고    scopus 로고
    • Multiscale numerical methods for singularly-perturbed convection diffusion equations
    • Park P., and Hou T.Y. Multiscale numerical methods for singularly-perturbed convection diffusion equations. Intl. J. Comput. Meth. 1 1 (2004) 17-65
    • (2004) Intl. J. Comput. Meth. , vol.1 , Issue.1 , pp. 17-65
    • Park, P.1    Hou, T.Y.2
  • 13
    • 85190802906 scopus 로고    scopus 로고
    • Y. Efendiev, V. Ginting, T.Y. Hou, R. Ewing, Accurate multiscale finite element methods for two-phase flow simulations, J. Comput. Phys, submitted.
  • 14
    • 28444496198 scopus 로고    scopus 로고
    • Generalized finite element methods: main ideas, results and perspective
    • Babuska I., Banerjee U., and Osborn J. Generalized finite element methods: main ideas, results and perspective. Int. J. Comput. Meth. 1 (2004) 67-103
    • (2004) Int. J. Comput. Meth. , vol.1 , pp. 67-103
    • Babuska, I.1    Banerjee, U.2    Osborn, J.3
  • 15
    • 18144399279 scopus 로고    scopus 로고
    • Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions
    • Franca L.P., Madureira A.L., and Valentin F. Towards multiscale functions: enriching finite element spaces with local but not bubble-like functions. Comp. Meth. Appl. Mech. Eng. 194 27-29 (2005) 3006-3021
    • (2005) Comp. Meth. Appl. Mech. Eng. , vol.194 , Issue.27-29 , pp. 3006-3021
    • Franca, L.P.1    Madureira, A.L.2    Valentin, F.3
  • 16
    • 0031244944 scopus 로고    scopus 로고
    • A state-of-the-art report on computational stochastic mechanics
    • Pradlwarter H.J., and Schueller G.I. A state-of-the-art report on computational stochastic mechanics. Probabil. Eng. Mech. 12 4 (1997) 197-322
    • (1997) Probabil. Eng. Mech. , vol.12 , Issue.4 , pp. 197-322
    • Pradlwarter, H.J.1    Schueller, G.I.2
  • 17
    • 85190766601 scopus 로고    scopus 로고
    • T. Hisada, S. Nakagiri, Role of stochastic finite element methods in structural safety and reliability, in: Proceedings of 4th International Conference on Structural Safety and Reliability, Kobe, Japan, 1985, pp. 385-394.
  • 18
    • 0023980492 scopus 로고
    • Response variability of stochastic finite element systems
    • Shinozuka M., and Deodatis G. Response variability of stochastic finite element systems. J. Eng. Mech. (ASCE) 114 3 (1988) 499-519
    • (1988) J. Eng. Mech. (ASCE) , vol.114 , Issue.3 , pp. 499-519
    • Shinozuka, M.1    Deodatis, G.2
  • 19
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D., and Karniadakis G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos. J. Comput. Phys. 187 (2003) 137-167
    • (2003) J. Comput. Phys. , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.E.2
  • 21
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of fourier hermite functionals
    • Cameron R.H., and Martin W.T. The orthogonal development of nonlinear functionals in series of fourier hermite functionals. Ann. Math. 48 (1947) 385-392
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 23
    • 0035506770 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow I. Basic formulation
    • Le Maître O.P., Kino O.M., Najm H.N., and Ghanem R. A stochastic projection method for fluid flow I. Basic formulation. J. Comput. Phys. 173 (2001) 481-511
    • (2001) J. Comput. Phys. , vol.173 , pp. 481-511
    • Le Maître, O.P.1    Kino, O.M.2    Najm, H.N.3    Ghanem, R.4
  • 24
    • 0036742814 scopus 로고    scopus 로고
    • A stochastic projection method for fluid flow II. Random process
    • Le Maître O.P., Reagan M., Ghanem R., and Kino O.M. A stochastic projection method for fluid flow II. Random process. J. Comput. Phys. 181 (2002) 9-44
    • (2002) J. Comput. Phys. , vol.181 , pp. 9-44
    • Le Maître, O.P.1    Reagan, M.2    Ghanem, R.3    Kino, O.M.4
  • 25
    • 0011074291 scopus 로고    scopus 로고
    • Stochastic modeling of flow-structure interactions using generalized polynomial chaos
    • Xiu D., Lucor D., Su C.H., and Karniadakis G.E. Stochastic modeling of flow-structure interactions using generalized polynomial chaos. J. Fluids. Eng. 125 (2001) 51-59
    • (2001) J. Fluids. Eng. , vol.125 , pp. 51-59
    • Xiu, D.1    Lucor, D.2    Su, C.H.3    Karniadakis, G.E.4
  • 27
    • 21244447771 scopus 로고    scopus 로고
    • Numerical homogenization of nonlinear random parabolic operators
    • Efendiev Y., and Pankov A. Numerical homogenization of nonlinear random parabolic operators. SIAM MMS 2 2 (2004) 237-268
    • (2004) SIAM MMS , vol.2 , Issue.2 , pp. 237-268
    • Efendiev, Y.1    Pankov, A.2
  • 28
    • 16244408322 scopus 로고    scopus 로고
    • Numerical homogenization and correctors for random nonlinear elliptic equations
    • Efendiev Y., and Pankov A. Numerical homogenization and correctors for random nonlinear elliptic equations. SIAM J. Appl. Math. 65 1 (2004) 43-68
    • (2004) SIAM J. Appl. Math. , vol.65 , Issue.1 , pp. 43-68
    • Efendiev, Y.1    Pankov, A.2
  • 29
    • 0029405472 scopus 로고
    • Multiscale phenomena: Green's functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origin of stabilized methods
    • Hughes T.J.R. Multiscale phenomena: Green's functions, the dirichlet-to-neumann formulation, subgrid scale models, bubbles and the origin of stabilized methods. Comp. Meth. Appl. Mech. Eng. 127 (1995) 387-401
    • (1995) Comp. Meth. Appl. Mech. Eng. , vol.127 , pp. 387-401
    • Hughes, T.J.R.1
  • 31
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite element formulation
    • Ghanem R. Ingredients for a general purpose stochastic finite element formulation. Comp. Meth. Appl. Mech. Eng. 168 (1999) 19-34
    • (1999) Comp. Meth. Appl. Mech. Eng. , vol.168 , pp. 19-34
    • Ghanem, R.1
  • 32
    • 8744246329 scopus 로고    scopus 로고
    • Variational multiscale stabilized fem formulations for transport equations: stochastic advection-diffusion and incompressible stochastic navier-stokes equations
    • Velamur Asokan B., and Zabaras N. Variational multiscale stabilized fem formulations for transport equations: stochastic advection-diffusion and incompressible stochastic navier-stokes equations. J. Computat. Phys. 202 (2004) 94-133
    • (2004) J. Computat. Phys. , vol.202 , pp. 94-133
    • Velamur Asokan, B.1    Zabaras, N.2
  • 33
    • 19044387138 scopus 로고    scopus 로고
    • Using stochastic analysis to capture unstable equilibrium in natural convection
    • Velamur Asokan B., and Zabaras N. Using stochastic analysis to capture unstable equilibrium in natural convection. J. Computat. Phys. 208 (2005) 134-153
    • (2005) J. Computat. Phys. , vol.208 , pp. 134-153
    • Velamur Asokan, B.1    Zabaras, N.2
  • 35
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener N. The homogeneous chaos. Am. J. Math. 60 (1930) 897-936
    • (1930) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 36
    • 1142296114 scopus 로고    scopus 로고
    • Spectral polynomial chaos solutions of the stochastic advection equation
    • Jardak M., Su C.-H., and Karniadakis G.E. Spectral polynomial chaos solutions of the stochastic advection equation. J. Sci. Comput. 17 (2002) 319-338
    • (2002) J. Sci. Comput. , vol.17 , pp. 319-338
    • Jardak, M.1    Su, C.-H.2    Karniadakis, G.E.3
  • 37
    • 85190816768 scopus 로고    scopus 로고
    • X. Wan, G.E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Tech. rep., BrownSC-2005-07, Brown University, 2005.
  • 39
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24 2 (2002) 619-644
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 40
    • 1142304457 scopus 로고    scopus 로고
    • On the accuracy of the polynomial chaos expansion
    • Field Jr. R.V., and Grigoriu M. On the accuracy of the polynomial chaos expansion. Probabil. Eng. Mech. 19 (2004) 65-80
    • (2004) Probabil. Eng. Mech. , vol.19 , pp. 65-80
    • Field Jr., R.V.1    Grigoriu, M.2
  • 42
    • 3042732038 scopus 로고    scopus 로고
    • Capturing small scales in elliptic problems using a residual-free bubbles finite element method
    • Sangalli G. Capturing small scales in elliptic problems using a residual-free bubbles finite element method. SIAM MMS 1 3 (2003) 485-503
    • (2003) SIAM MMS , vol.1 , Issue.3 , pp. 485-503
    • Sangalli, G.1
  • 43
    • 13844298952 scopus 로고    scopus 로고
    • Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels
    • Aarnes J.E., Kippe V., and Lie K.A. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Res. 28 3 (2005) 257-271
    • (2005) Adv. Water Res. , vol.28 , Issue.3 , pp. 257-271
    • Aarnes, J.E.1    Kippe, V.2    Lie, K.A.3
  • 44
    • 33748432259 scopus 로고    scopus 로고
    • Equation-free, multiscale computation for unsteady random diffusion
    • Xiu D., and Kevrekidis I.G. Equation-free, multiscale computation for unsteady random diffusion. SIAM MMS 4 3 (2005) 915-935
    • (2005) SIAM MMS , vol.4 , Issue.3 , pp. 915-935
    • Xiu, D.1    Kevrekidis, I.G.2
  • 45
    • 0038824886 scopus 로고    scopus 로고
    • Microscopic/stochastic timesteppers and coarse control: a kinetic monte carlo example
    • Siettos C.I., Armaou A., Makeev A.G., and Kevrekidis I.G. Microscopic/stochastic timesteppers and coarse control: a kinetic monte carlo example. AIChE J. 49 7 (2003) 1922-1926
    • (2003) AIChE J. , vol.49 , Issue.7 , pp. 1922-1926
    • Siettos, C.I.1    Armaou, A.2    Makeev, A.G.3    Kevrekidis, I.G.4
  • 46
    • 0037104864 scopus 로고    scopus 로고
    • "Coarse" integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods
    • Gear W., Kevrekidis I.G., and Theodoropoulos C. "Coarse" integration/bifurcation analysis via microscopic simulators: micro-Galerkin methods. Comp. Chem. Eng. 26 (2002) 941-963
    • (2002) Comp. Chem. Eng. , vol.26 , pp. 941-963
    • Gear, W.1    Kevrekidis, I.G.2    Theodoropoulos, C.3
  • 47
    • 3142610894 scopus 로고    scopus 로고
    • Stochastic inverse heat conduction using a spectral approach
    • Velamur Asokan B., and Zabaras N. Stochastic inverse heat conduction using a spectral approach. Intl. J. Num. Meth. Eng. 60 9 (2004) 1569-1593
    • (2004) Intl. J. Num. Meth. Eng. , vol.60 , Issue.9 , pp. 1569-1593
    • Velamur Asokan, B.1    Zabaras, N.2
  • 48
    • 0141792397 scopus 로고    scopus 로고
    • A new stochastic approach to transient heat conduction modeling with uncertainty
    • Xiu D., and Karniadakis G.E. A new stochastic approach to transient heat conduction modeling with uncertainty. Int. J. Heat Mass Transf. 46 24 (2003) 4681-4693
    • (2003) Int. J. Heat Mass Transf. , vol.46 , Issue.24 , pp. 4681-4693
    • Xiu, D.1    Karniadakis, G.E.2
  • 49
    • 85190766442 scopus 로고    scopus 로고
    • C. Carter, Available from: .


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.