메뉴 건너뛰기




Volumn 2, Issue 2, 2004, Pages 237-268

Numerical homogenization of nonlinear random parabolic operators

Author keywords

Finite element; Homogenization; Multiscale; Nonlinear; Parabolic; Random; Upscaling

Indexed keywords

FINITE ELEMENT METHOD; HOMOGENIZATION METHOD; NONLINEAR EQUATIONS; NUMERICAL METHODS;

EID: 21244447771     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/030600266     Document Type: Article
Times cited : (90)

References (23)
  • 1
    • 85021692477 scopus 로고
    • Existence and Meyers estimate for nonlinear parabolic variational inequalities
    • M. Biroli, Existence and Meyers estimate for nonlinear parabolic variational inequalities, Ricerche Mat., 36 (1987), pp. 11-33.
    • (1987) Ricerche Mat. , vol.36 , pp. 11-33
    • Biroli, M.1
  • 3
    • 84972572146 scopus 로고
    • Correctors for the homogenization of monotone operators
    • G. Dal Maso and A. Defranceschi, Correctors for the homogenization of monotone operators, Differential Integral Equations, 3 (1990), pp. 1151-1166.
    • (1990) Differential Integral Equations , vol.3 , pp. 1151-1166
    • Dal Maso, G.1    Defranceschi, A.2
  • 5
    • 84941461568 scopus 로고
    • Regularity of solutions of nonlinear degenerate parabolic systems
    • E. DiBenedetto and A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math., 349 (1984), pp. 83-128.
    • (1984) J. Reine Angew. Math. , vol.349 , pp. 83-128
    • DiBenedetto, E.1    Friedman, A.2
  • 6
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multi-scale methods
    • W. E and E. Engquist, The heterogeneous multi-scale methods, Comm. Math. Sci., 1 (2003), pp. 87-132.
    • (2003) Comm. Math. Sci. , vol.1 , pp. 87-132
    • Engquist, E.1
  • 8
    • 84860092627 scopus 로고    scopus 로고
    • Meyers type estimates for approximate solutions of nonlinear elliptic equations and their applications
    • submitted
    • Y. Efendiev and A. Pankov, Meyers type estimates for approximate solutions of nonlinear elliptic equations and their applications, Numer. Math., submitted.
    • Numer. Math.
    • Efendiev, Y.1    Pankov, A.2
  • 9
    • 34548555443 scopus 로고    scopus 로고
    • Numerical homogenization of monotone elliptic operators
    • Y. Efendiev and A. Pankov, Numerical homogenization of monotone elliptic operators, Multiscale Model. Simul., 2 (2003), pp. 62-79.
    • (2003) Multiscale Model. Simul. , vol.2 , pp. 62-79
    • Efendiev, Y.1    Pankov, A.2
  • 10
    • 0028416333 scopus 로고
    • Convection enhanced diffusion for periodic flows
    • A. Fannjiang and G. Papanicolaou, Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math., 54 (1994), pp. 333-408.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 333-408
    • Fannjiang, A.1    Papanicolaou, G.2
  • 11
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • T. Y. Hou and X. H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.H.2
  • 15
    • 0347601794 scopus 로고    scopus 로고
    • Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena
    • A. J. Majda and P. R. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep., 314 (1999), pp. 237-574.
    • (1999) Phys. Rep. , vol.314 , pp. 237-574
    • Majda, A.J.1    Kramer, P.R.2
  • 16
    • 84972585107 scopus 로고
    • Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions
    • N. G. Meyers and A. Elcrat, Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions, Duke Math. J., 42 (1975), pp. 121-136.
    • (1975) Duke Math. J. , vol.42 , pp. 121-136
    • Meyers, N.G.1    Elcrat, A.2
  • 17
    • 52549098647 scopus 로고    scopus 로고
    • Homogenization of a nonlinear degenerate parabolic differential equation
    • paper 17
    • A. K. Nandakumaran and M. Rajesh, Homogenization of a nonlinear degenerate parabolic differential equation, Electron. J. Differential Equations, 9 (2001), paper 17.
    • (2001) Electron. J. Differential Equations , vol.9
    • Nandakumaran, A.K.1    Rajesh, M.2
  • 20
    • 0003291397 scopus 로고    scopus 로고
    • Monotone operators in banach space and nonlinear partial differential equations
    • AMS, Providence, RI
    • R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Math. Surveys Monogr. 49, AMS, Providence, RI, 1997.
    • (1997) Math. Surveys Monogr. , vol.49
    • Showalter, R.E.1
  • 21
    • 0003213458 scopus 로고
    • Methods for analysis of nonlinear elliptic boundary value problems
    • AMS, Providence, RI
    • I. V. Skrypnik, Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, Transl. Math. Monogr. 139, AMS, Providence, RI, 1994.
    • (1994) Transl. Math. Monogr. , vol.139
    • Skrypnik, I.V.1
  • 22
    • 0034557059 scopus 로고    scopus 로고
    • Correctors for the homogenization of monotone parabolic operators
    • N. Svanstedt, Correctors for the homogenization of monotone parabolic operators, J. Nonlinear Math. Phys., 7 (2000), pp. 268-283.
    • (2000) J. Nonlinear Math. Phys. , vol.7 , pp. 268-283
    • Svanstedt, N.1
  • 23
    • 16244398426 scopus 로고
    • Averaging of parabolic operators
    • V. V. Zhikov, S. M. Kozlov, and O. A. Oleǐnik, Averaging of parabolic operators, Trudy Moskov. Mat. Obshch., 45 (1982), pp. 182-236.
    • (1982) Trudy Moskov. Mat. Obshch. , vol.45 , pp. 182-236
    • Zhikov, V.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.