메뉴 건너뛰기




Volumn 14, Issue 1, 2010, Pages 31-53

A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations

Author keywords

Degenerate parabolic; Doubly degenerate diffusion; Doubly nonlinear; Galerkin method nonlinear diffusion; Overland flow; Shallow water equations; Wetland modeling

Indexed keywords

ACCURACY ASSESSMENT; COMPUTER SIMULATION; DIFFUSION; EXPERIMENTAL STUDY; FINITE ELEMENT METHOD; FLOW MODELING; GALERKIN METHOD; GEOSTATISTICS; LAPLACE TRANSFORM; NONLINEARITY; NUMERICAL MODEL; OVERLAND FLOW; POROUS MEDIUM; SHALLOW-WATER EQUATION; WETLAND;

EID: 77952877284     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-009-9131-4     Document Type: Article
Times cited : (31)

References (37)
  • 1
    • 50849144038 scopus 로고    scopus 로고
    • On the difussive wave approximation of the shallow water equations
    • Alonso, R., Santillana, M., Dawson, C.: On the difussive wave approximation of the shallow water equations. Eur. J. Appl. Math. 19(5), 575-606 (2008).
    • (2008) Eur. J. Appl. Math. , vol.19 , Issue.5 , pp. 575-606
    • Alonso, R.1    Santillana, M.2    Dawson, C.3
  • 2
    • 0000325197 scopus 로고    scopus 로고
    • A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media
    • Arbogast, T., Wheeler, M. F., Zhang, N. Y.: A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J. Numer. Anal. 33(4), 1669-1687 (1996).
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.4 , pp. 1669-1687
    • Arbogast, T.1    Wheeler, M.F.2    Zhang, N.Y.3
  • 3
    • 0008563110 scopus 로고
    • Étude d'une équation doublement non linéaire
    • Bamberger, A.: Étude d'une équation doublement non linéaire. J. Funct. Anal. 24, 148-155 (1977).
    • (1977) J. Funct. Anal. , vol.24 , pp. 148-155
    • Bamberger, A.1
  • 4
    • 0028413859 scopus 로고
    • Finite element approximation of the parabolic p-laplacian
    • Barrett, J. W., Liu, W. B.: Finite element approximation of the parabolic p-laplacian. SIAM J. Numer. Anal. 31(2), 413-428 (1994).
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.2 , pp. 413-428
    • Barrett, J.W.1    Liu, W.B.2
  • 5
  • 7
    • 0033407951 scopus 로고    scopus 로고
    • Entropy solutions for nonlinear degenerate problems
    • Carrillo, J.: Entropy solutions for nonlinear degenerate problems. Arch. Ration. Mech. Anal. 147(4), 269-361 (1999).
    • (1999) Arch. Ration. Mech. Anal. , vol.147 , Issue.4 , pp. 269-361
    • Carrillo, J.1
  • 10
    • 0002210953 scopus 로고
    • Homogeneous diffusion in ℝ with power-like nonlinear diffusivity
    • Esteban, J. R., Vázquez, J. L.: Homogeneous diffusion in ℝ with power-like nonlinear diffusivity. Arch. Rat. Mech. Anal. 103, 39-80 (1988).
    • (1988) Arch. Rat. Mech. Anal. , vol.103 , pp. 39-80
    • Esteban, J.R.1    Vázquez, J.L.2
  • 12
    • 0034402365 scopus 로고    scopus 로고
    • Discrete approximations of bv solutions to doubly nonlinear degenerate parabolic equations
    • Evje, S., Karlsen, K.: Discrete approximations of bv solutions to doubly nonlinear degenerate parabolic equations. Numer. Math. 86(3), 377-417 (2000).
    • (2000) Numer. Math. , vol.86 , Issue.3 , pp. 377-417
    • Evje, S.1    Karlsen, K.2
  • 13
    • 0142087695 scopus 로고    scopus 로고
    • Galerkin finite element method for a class of porous medium equations
    • Fadimba, K. B., Sharpley, R. C.: Galerkin finite element method for a class of porous medium equations. Nonlinear Anal. Real World Appl. 5, 355-387 (2004).
    • (2004) Nonlinear Anal. Real World Appl. , vol.5 , pp. 355-387
    • Fadimba, K.B.1    Sharpley, R.C.2
  • 14
    • 0031239756 scopus 로고    scopus 로고
    • A 2-d diffusion based, wetland flow model
    • Feng, K., Molz, F. J.: A 2-d diffusion based, wetland flow model. J. Hydrol. 196, 230-250 (1997).
    • (1997) J. Hydrol. , vol.196 , pp. 230-250
    • Feng, K.1    Molz, F.J.2
  • 15
    • 0030483135 scopus 로고    scopus 로고
    • A conservative finite elements approach to overland flow: The control volume finite element formulation
    • Di Giammarco, P., Todini, E., Lamberti, P.: A conservative finite elements approach to overland flow: the control volume finite element formulation. J. Hydrol. 175, 267-291 (1996).
    • (1996) J. Hydrol. , vol.175 , pp. 267-291
    • Di Giammarco, P.1    Todini, E.2    Lamberti, P.3
  • 16
    • 0002973412 scopus 로고
    • Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires
    • Grange, O., Mignot, F.: Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires. J. Funct. Anal. 11, 77-92 (1972).
    • (1972) J. Funct. Anal. , vol.11 , pp. 77-92
    • Grange, O.1    Mignot, F.2
  • 17
    • 55349091064 scopus 로고    scopus 로고
    • Finite element runge-kutta discretizations of porous medium-type equations
    • Hansen, E., Ostermann, A.: Finite element runge-kutta discretizations of porous medium-type equations. SIAM J. Numer. Anal. 46(4), 1769-1779 (2008).
    • (2008) SIAM J. Numer. Anal. , vol.46 , Issue.4 , pp. 1769-1779
    • Hansen, E.1    Ostermann, A.2
  • 18
    • 33847231933 scopus 로고    scopus 로고
    • Philadelphia: Society for Industrial and Applied Mathematics
    • Hartman, P.: Ordinary Differential Equations. Society for Industrial and Applied Mathematics, Philadelphia (2002).
    • (2002) Ordinary Differential Equations
    • Hartman, P.1
  • 20
    • 0035982250 scopus 로고    scopus 로고
    • A numerical approach to degenerate parabolic equations
    • Yong, W., Pop, I. S.: A numerical approach to degenerate parabolic equations. Numer. Math. 92(2), 357-381 (2002).
    • (2002) Numer. Math. , vol.92 , Issue.2 , pp. 357-381
    • Yong, W.1    Pop, I.S.2
  • 21
    • 0030515336 scopus 로고    scopus 로고
    • On the existence of solutions of the Cauchy problem for a doubly nonlinear parabolic equation
    • Ishige, K.: On the existence of solutions of the Cauchy problem for a doubly nonlinear parabolic equation. SIAM J. Math. Anal. 27(5), 1235-1260 (1996).
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.5 , pp. 1235-1260
    • Ishige, K.1
  • 22
    • 0342534626 scopus 로고
    • Fundamental studies of runoff analysis by characteristics
    • In: Bulletin, Kyoto University, Kyoto, Japan
    • Iwagaki, Y.: Fundamental studies of runoff analysis by characteristics. In: Bulletin, vol. 10, p. 25. Disaster Prevention Res. Inst., Kyoto University, Kyoto, Japan (1955).
    • (1955) Disaster Prevention Res. Inst. , vol.10 , pp. 25
    • Iwagaki, Y.1
  • 23
    • 0005717590 scopus 로고
    • Galerkin methods for parabolic equations
    • Douglas, J. Jr., Dupont, T. F.: Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7, 575-626 (1970).
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 575-626
    • Douglas Jr., J.1    Dupont, T.F.2
  • 25
    • 0001278368 scopus 로고
    • Approximation of degenerate parabolic problems using numerical integration
    • Nochetto, R. H., Verdi, C.: Approximation of degenerate parabolic problems using numerical integration. SIAM J. Numer. Anal. 25, 784-814 (1988).
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 784-814
    • Nochetto, R.H.1    Verdi, C.2
  • 26
    • 0017944710 scopus 로고
    • Aplicability of kinematic and diffusion models
    • Ponce, V. M., Li, R. M., Simons, D. B.: Aplicability of kinematic and diffusion models. J. Hydraul. Div. 104, 353-360 (1978).
    • (1978) J. Hydraul. Div. , vol.104 , pp. 353-360
    • Ponce, V.M.1    Li, R.M.2    Simons, D.B.3
  • 27
    • 0017723656 scopus 로고
    • Shallow wave propagation in open channel flow
    • Ponce, V. M., Simons, D. B.: Shallow wave propagation in open channel flow. J. Hydraul. Div. 103, 1461-1476 (1977).
    • (1977) J. Hydraul. Div. , vol.103 , pp. 1461-1476
    • Ponce, V.M.1    Simons, D.B.2
  • 28
    • 0000854377 scopus 로고
    • Sur la résolution de certaines équations paraboliques non linéaires
    • Raviart, P. A.: Sur la résolution de certaines équations paraboliques non linéaires. J. Funct. Anal. 5, 299-328 (1970).
    • (1970) J. Funct. Anal. , vol.5 , pp. 299-328
    • Raviart, P.A.1
  • 29
    • 84966221941 scopus 로고
    • Numerical methods for flows through porous media. I
    • Rose, M. E.: Numerical methods for flows through porous media. I. Math. Comput. 40(162), 435-467 (1983).
    • (1983) Math. Comput. , vol.40 , Issue.162 , pp. 435-467
    • Rose, M.E.1
  • 30
    • 0002124686 scopus 로고    scopus 로고
    • Optimal rates of convergence for degenerate parabolic problems in two dimensions
    • Rulla, J., Walkington, N. J.: Optimal rates of convergence for degenerate parabolic problems in two dimensions. SIAM J. Numer. Anal. 33(1), 56-67 (1996).
    • (1996) SIAM J. Numer. Anal. , vol.33 , Issue.1 , pp. 56-67
    • Rulla, J.1    Walkington, N.J.2
  • 32
    • 0000256942 scopus 로고
    • Shallow flow of water through non-submerged vegetation
    • Turner, A. K., Chanmeesri, N.: Shallow flow of water through non-submerged vegetation. Agric. Water Manag. 8, 375-385 (1984).
    • (1984) Agric. Water Manag. , vol.8 , pp. 375-385
    • Turner, A.K.1    Chanmeesri, N.2
  • 35
    • 0001287713 scopus 로고
    • 2 error estimates for galerkin approximations to parabolic partial differential equations
    • 2 error estimates for galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal. 10(4), 723-759 (1973).
    • (1973) SIAM J. Numer. Anal. , vol.10 , Issue.4 , pp. 723-759
    • Wheeler, M.F.1
  • 36
    • 0016879782 scopus 로고
    • Numerical simulation of a two dimensional flood wave propagation due to dam failure
    • Xanthopoulos, Th., Koutitas, Ch.: Numerical simulation of a two dimensional flood wave propagation due to dam failure. J. Hydraul. Res. 14(4), 321-331 (1976).
    • (1976) J. Hydraul. Res. , vol.14 , Issue.4 , pp. 321-331
    • Xanthopoulos, T.1    Koutitas, C.2
  • 37
    • 0024846605 scopus 로고
    • Modeling of two-dimensional overland flow
    • Zhang, W., Cundy, T. W.: Modeling of two-dimensional overland flow. Water Resour. Res. 25, 2019-2035 (1989).
    • (1989) Water Resour. Res. , vol.25 , pp. 2019-2035
    • Zhang, W.1    Cundy, T.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.