메뉴 건너뛰기




Volumn 64, Issue 2, 2000, Pages 157-182

Finite Volume Element Approximations of Nonlocal in Time One-Dimensional Flows in Porous Media

Author keywords

Finite volume method; Integro differential equation; Parabolic equation

Indexed keywords


EID: 0141716196     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s006070050007     Document Type: Article
Times cited : (41)

References (29)
  • 1
    • 0347882290 scopus 로고    scopus 로고
    • Long-time stability of finite element approximations for parabolic equations with memory
    • to appear
    • Allegretto, W., Lin, Y., Zhou, A.: Long-time stability of finite element approximations for parabolic equations with memory. Numer. Meth. PDE's, (to appear).
    • Numer. Meth. PDE's
    • Allegretto, W.1    Lin, Y.2    Zhou, A.3
  • 2
    • 0032296181 scopus 로고    scopus 로고
    • Long time behavior of backward difference type methods for parabolic equations with memory in Banach space
    • Bakaev, N., Larsson, S., Thomée, V.: Long time behavior of backward difference type methods for parabolic equations with memory in Banach space. East-West J. Numer. Math. 6, 185-206 (1998).
    • (1998) East-West J. Numer. Math. , vol.6 , pp. 185-206
    • Bakaev, N.1    Larsson, S.2    Thomée, V.3
  • 3
    • 0023401301 scopus 로고
    • Some error estimates for the box method
    • Bank, R., Rose, D.: Some error estimates for the box method. SIAM J. Numer. Math. 24, 777-787 (1987).
    • (1987) SIAM J. Numer. Math. , vol.24 , pp. 777-787
    • Bank, R.1    Rose, D.2
  • 4
    • 0003550186 scopus 로고
    • The numerical solution for Volterra equations
    • North Holland, Amsterdam
    • Brunner, H., van der Houwen, P.: The numerical solution for Volterra equations. CWI Monographs, vol. 3. North Holland, Amsterdam, 1986.
    • (1986) CWI Monographs , vol.3
    • Brunner, H.1    Houwen, V.D.2    P3
  • 5
    • 0001063435 scopus 로고
    • On the finite volume element method
    • Cai, Z.: On the finite volume element method. Numer. Math. 58, 713-735 (1991).
    • (1991) Numer. Math. , vol.58 , pp. 713-735
    • Cai, Z.1
  • 6
    • 51249176168 scopus 로고
    • 1-projection and Galerkin methods for nonlinear parabolic integro-differential equations
    • 1-projection and Galerkin methods for nonlinear parabolic integro-differential equations. Calcolo 25, 187-201 (1988).
    • (1988) Calcolo , vol.25 , pp. 187-201
    • Cannon, J.1    Lin, Y.2
  • 7
    • 0025445438 scopus 로고
    • 2-error estimates for finite element methods for nonlinear diffusion equations with memory
    • 2-error estimates for finite element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal. 27, 595-607 (1990).
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 595-607
    • Cannon, J.1    Lin, Y.2
  • 8
    • 0000661816 scopus 로고
    • The lumped mass finite element method for a parabolic problem
    • Chen, C., Thomée, V.: The lumped mass finite element method for a parabolic problem. J. Austral. Math. Soc. Ser. B 26, 329-354 (1985).
    • (1985) J. Austral. Math. Soc. Ser. B , vol.26 , pp. 329-354
    • Chen, C.1    Thomée, V.2
  • 9
    • 0027683759 scopus 로고
    • Nonlocal dispersion in media with continuously evolving scales of heterogeneity
    • Cushman, J., Ginn, T.: Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Trans. Porous Media 13, 123-138 (1993).
    • (1993) Trans. Porous Media , vol.13 , pp. 123-138
    • Cushman, J.1    Ginn, T.2
  • 10
    • 0028666604 scopus 로고
    • The significance of heterogeneity of evolving scales to transport in porous formations
    • Dagan, G.: The significance of heterogeneity of evolving scales to transport in porous formations. Water Resources Res. 30, 3327-3336 (1994).
    • (1994) Water Resources Res. , vol.30 , pp. 3327-3336
    • Dagan, G.1
  • 12
    • 0347882287 scopus 로고
    • Homogeneous difference schemes for one dimensional elliptic problems with generalized solutions
    • Godev, K., Lazarov, R., Makarov, V., Samarskii, A.: Homogeneous difference schemes for one dimensional elliptic problems with generalized solutions. Math. USSR Sbornik 59, 155-179 (1988).
    • (1988) Math. USSR Sbornik , vol.59 , pp. 155-179
    • Godev, K.1    Lazarov, R.2    Makarov, V.3    Samarskii, A.4
  • 13
    • 0024776669 scopus 로고
    • On first and second order box schemes
    • Hackbusch, W.: On first and second order box schemes. Computing 41, 277-296 (1989).
    • (1989) Computing , vol.41 , pp. 277-296
    • Hackbusch, W.1
  • 14
    • 0006191866 scopus 로고
    • Finite difference on irregular networks, a generalized approach to second order problems
    • Basel: Birkhäuser
    • Heinrich, B.: Finite difference on irregular networks, A generalized approach to second order problems. ISNM 82. Basel: Birkhäuser 1987.
    • (1987) ISNM , vol.82
    • Heinrich, B.1
  • 15
    • 0028755634 scopus 로고
    • Finite volume element methods with local refinement for convection-diffusion problems
    • Lazarov, R., Mishev, I., Vassilevski, P.: Finite volume element methods with local refinement for convection-diffusion problems. Computing 53, 33-57 (1994).
    • (1994) Computing , vol.53 , pp. 33-57
    • Lazarov, R.1    Mishev, I.2    Vassilevski, P.3
  • 17
    • 0042742929 scopus 로고    scopus 로고
    • On maximum norm estimates for Ritz-Volterra projections and applications to some time-dependent problems
    • Lin, Y.: On maximum norm estimates for Ritz-Volterra projections and applications to some time-dependent problems. J. Comp. Math. 15, 159-178 (1997).
    • (1997) J. Comp. Math. , vol.15 , pp. 159-178
    • Lin, Y.1
  • 18
    • 33845695097 scopus 로고    scopus 로고
    • Semi-discrete finite element approximations for linear parabolic integro-differential equations with integrable kernels
    • to appear
    • Lin, Y.: Semi-discrete finite element approximations for linear parabolic integro-differential equations with integrable kernels. J. Int. Eq. Appl. (to appear).
    • J. Int. Eq. Appl.
    • Lin, Y.1
  • 19
    • 0026204786 scopus 로고
    • Ritz-Volterra projection onto finite element spaces and application to integro-differential and related equations
    • Lin, Y., Thomée, V., Wahlbin, L.: Ritz-Volterra projection onto finite element spaces and application to integro-differential and related equations. SIAM J. Numer. Anal. 28, 1047-107 (1991).
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1047-1107
    • Lin, Y.1    Thomée, V.2    Wahlbin, L.3
  • 21
    • 0037827941 scopus 로고
    • Numerical methods for hyperbolic and parabolic integro-differential equations
    • Pani, A., Thomée, V., Wahlbin, L.: Numerical methods for hyperbolic and parabolic integro-differential equations. J. Int. Eq. Appl. 4, 533-584 (1992).
    • (1992) J. Int. Eq. Appl. , vol.4 , pp. 533-584
    • Pani, A.1    Thomée, V.2    Wahlbin, L.3
  • 24
    • 0041741372 scopus 로고
    • A non-local in time model for radionuclides propagation in Stokes fluids. Dynamics of fluids with free boundaries
    • Shelukhin, V.: A non-local in time model for radionuclides propagation in Stokes fluids. Dynamics of fluids with free boundaries. Siberian Branch of the Russian Academy of Sciences, Inst. of Hydrodynamics 107, 180-193 (1993).
    • (1993) Siberian Branch of the Russian Academy of Sciences, Inst. of Hydrodynamics , vol.107 , pp. 180-193
    • Shelukhin, V.1
  • 25
    • 0001406595 scopus 로고
    • Time-discretization of an integro-differential equations of parabolic type
    • Sloan, I., Thomée, V.: Time-discretization of an integro-differential equations of parabolic type, SIAM J. Numer. Math. 23, 1052-1061 (1986).
    • (1986) SIAM J. Numer. Math. , vol.23 , pp. 1052-1061
    • Sloan, I.1    Thomée, V.2
  • 27
    • 0000898457 scopus 로고
    • Homogeneous difference schemes on nonuniform nets
    • Tikhonov, A., Samarskii, A.: Homogeneous difference schemes on nonuniform nets. Zh. Vychisl. Mat. Mat. Fiz., 2, 812-832 (1962).
    • (1962) Zh. Vychisl. Mat. Mat. Fiz. , vol.2 , pp. 812-832
    • Tikhonov, A.1    Samarskii, A.2
  • 28
    • 0003208045 scopus 로고
    • Galerkin finite element methods for parabolic problems
    • Berlin Heidelberg New York Tokyo: Springer
    • Thomée, V.: Galerkin finite element methods for parabolic problems. Lecture Notes in Mathematics, 1054, Berlin Heidelberg New York Tokyo: Springer, 1984.
    • (1984) Lecture Notes in Mathematics , vol.1054
    • Thomée, V.1
  • 29
    • 84968518942 scopus 로고
    • Long-time numerical solution of a parabolic equation with memory
    • Thomée, V., Wahlbin, L.: Long-time numerical solution of a parabolic equation with memory. Math. Comp. 62, 477-496 (1994).
    • (1994) Math. Comp. , vol.62 , pp. 477-496
    • Thomée, V.1    Wahlbin, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.