메뉴 건너뛰기




Volumn 30, Issue 3, 2007, Pages 555-575

Local discontinuous Galerkin approximations to Richards' equation

Author keywords

Adaptive; Local discontinuous Galerkin; Method of lines; Unsaturated flow

Indexed keywords

APPROXIMATION THEORY; INTEGRATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NUMERICAL METHODS;

EID: 33846373762     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2006.04.011     Document Type: Article
Times cited : (40)

References (92)
  • 1
    • 0025199135 scopus 로고
    • Self-adaptive hierarchic finite element solution of the one-dimensional unsaturated flow equation
    • Abriola L.M., and Lang J.R. Self-adaptive hierarchic finite element solution of the one-dimensional unsaturated flow equation. Int J Numer Methods Fluids 10 (1990) 227-246
    • (1990) Int J Numer Methods Fluids , vol.10 , pp. 227-246
    • Abriola, L.M.1    Lang, J.R.2
  • 2
    • 0034306644 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for contaminant transport
    • Aizinger V., Dawson C.N., Cockburn B., and Castillo P. The local discontinuous Galerkin method for contaminant transport. Adv Water Resour 24 1 (2000) 73-87
    • (2000) Adv Water Resour , vol.24 , Issue.1 , pp. 73-87
    • Aizinger, V.1    Dawson, C.N.2    Cockburn, B.3    Castillo, P.4
  • 3
    • 33846396477 scopus 로고    scopus 로고
    • Allmaras SR, Giles MB. A coupled Euler/Navier-Stokes algorithm for 2-D unsteady transonic flows. In: Aerospace sciences meeting. vol. 17. Reno, NV; 1989.
  • 4
    • 11744378418 scopus 로고    scopus 로고
    • Enhanced cell-centered finite differences for elliptic equations on general geometry
    • Arbogast T., Dawson C.N., Keenan P.T., Wheeler M.F., and Yotov I. Enhanced cell-centered finite differences for elliptic equations on general geometry. SIAM J Sci Comput 19 2 (1998) 404-425
    • (1998) SIAM J Sci Comput , vol.19 , Issue.2 , pp. 404-425
    • Arbogast, T.1    Dawson, C.N.2    Keenan, P.T.3    Wheeler, M.F.4    Yotov, I.5
  • 5
    • 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., and 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 (1996) 1669-1687
    • (1996) SIAM J Numer Anal , vol.33 , Issue.4 , pp. 1669-1687
    • Arbogast, T.1    Wheeler, M.F.2    Zhang, N.Y.3
  • 6
    • 0025489065 scopus 로고
    • Mixed finite element methods for elliptic problems
    • Arnold D.N. Mixed finite element methods for elliptic problems. Comput Methods Appl Mech Eng 82 (1990) 281-300
    • (1990) Comput Methods Appl Mech Eng , vol.82 , pp. 281-300
    • Arnold, D.N.1
  • 7
    • 0036410391 scopus 로고    scopus 로고
    • Unified analysis of discontinuous Galerkin methods for elliptic problems
    • Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39 5 (2002) 1749-1779
    • (2002) SIAM J Numer Anal , vol.39 , Issue.5 , pp. 1749-1779
    • Arnold, D.N.1    Brezzi, F.2    Cockburn, B.3    Marini, L.D.4
  • 8
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J Comput Phys 131 (1997) 267-279
    • (1997) J Comput Phys , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 9
    • 27744438681 scopus 로고    scopus 로고
    • Higher order discontinuous Galerkin methods for flow and transport in porous media
    • Bnsch E. (Ed), Springer-Verlag, Berlin
    • Bastian P. Higher order discontinuous Galerkin methods for flow and transport in porous media. In: Bnsch E. (Ed). Challenges in scientific computing (2003), Springer-Verlag, Berlin
    • (2003) Challenges in scientific computing
    • Bastian, P.1
  • 10
    • 33846348715 scopus 로고    scopus 로고
    • Baumann CE, Oden JT. A discontinuous hp finite element method for the solution of the Euler equations of gas dynamics. In: Hafez M, Heinrich JC, editors. Proceedings of the 10th international conference on finite elements in fluids; 1998.
  • 11
    • 0345062335 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for convection-diffusion problems
    • Baumann C.E., and Oden J.T. A discontinuous hp finite element method for convection-diffusion problems. Comput Methods Appl Mech Eng 175 3-4 (1999) 311-341
    • (1999) Comput Methods Appl Mech Eng , vol.175 , Issue.3-4 , pp. 311-341
    • Baumann, C.E.1    Oden, J.T.2
  • 12
    • 2442605443 scopus 로고    scopus 로고
    • Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
    • Bause M., and Knabner P. Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods. Adv Water Resour 27 (2004) 565-581
    • (2004) Adv Water Resour , vol.27 , pp. 565-581
    • Bause, M.1    Knabner, P.2
  • 14
    • 0033587522 scopus 로고    scopus 로고
    • Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
    • Bergamaschi L., and Putti M. Mixed finite elements and Newton-type linearizations for the solution of Richards' equation. Int J Numer Methods Eng 45 (1999) 1025-1046
    • (1999) Int J Numer Methods Eng , vol.45 , pp. 1025-1046
    • Bergamaschi, L.1    Putti, M.2
  • 16
    • 0037252566 scopus 로고    scopus 로고
    • Performance of discontinuous Galerkin methods for elliptic PDEs
    • Castillo P. Performance of discontinuous Galerkin methods for elliptic PDEs. SIAM J Sci Comput 24 2 (2002) 524-547
    • (2002) SIAM J Sci Comput , vol.24 , Issue.2 , pp. 524-547
    • Castillo, P.1
  • 17
    • 0034548629 scopus 로고    scopus 로고
    • An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
    • Castillo P., Cockburn B., Perugia I., and Shotzau D. An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J Numer Anal 38 5 (2000) 1676-1706
    • (2000) SIAM J Numer Anal , vol.38 , Issue.5 , pp. 1676-1706
    • Castillo, P.1    Cockburn, B.2    Perugia, I.3    Shotzau, D.4
  • 18
    • 0025585761 scopus 로고
    • A general mass-conservative numerical solution for the unsaturated flow equation
    • Celia M.A., Bouloutas E.T., and Zarba R.L. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour Res 26 7 (1990) 1483-1496
    • (1990) Water Resour Res , vol.26 , Issue.7 , pp. 1483-1496
    • Celia, M.A.1    Bouloutas, E.T.2    Zarba, R.L.3
  • 19
    • 0000340987 scopus 로고
    • The local projection p0-p1-discontinuous-Galerkin finite-element method for scalar conservation-laws
    • Chavent G., and Cockburn B. The local projection p0-p1-discontinuous-Galerkin finite-element method for scalar conservation-laws. Rairo-Math Model Numer Anal-Model Math Anal Numer 23 4 (1989) 565-592
    • (1989) Rairo-Math Model Numer Anal-Model Math Anal Numer , vol.23 , Issue.4 , pp. 565-592
    • Chavent, G.1    Cockburn, B.2
  • 20
    • 0026398228 scopus 로고
    • A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems
    • Chavent G., and Roberts J.E. A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems. Adv Water Resour 14 6 (1991) 329-348
    • (1991) Adv Water Resour , vol.14 , Issue.6 , pp. 329-348
    • Chavent, G.1    Roberts, J.E.2
  • 21
    • 0000731022 scopus 로고
    • A finite-element method for the 1-D water flooding problem with gravity
    • Chavent G., and Salzano G. A finite-element method for the 1-D water flooding problem with gravity. J Comput Phys 45 3 (1982) 307-344
    • (1982) J Comput Phys , vol.45 , Issue.3 , pp. 307-344
    • Chavent, G.1    Salzano, G.2
  • 22
    • 0031141903 scopus 로고    scopus 로고
    • From single-phase to compositional flow: applicability of mixed finite elements
    • Chen Z., and Ewing R.E. From single-phase to compositional flow: applicability of mixed finite elements. Transp Porous Media 27 (1997) 225-242
    • (1997) Transp Porous Media , vol.27 , pp. 225-242
    • Chen, Z.1    Ewing, R.E.2
  • 23
    • 0000761187 scopus 로고    scopus 로고
    • Fully discrete finite element analysis of multiphase flow in groundwater hydrology
    • Chen Z., and Ewing R.E. Fully discrete finite element analysis of multiphase flow in groundwater hydrology. SIAM J Numer Anal 34 6 (1997) 2228-2253
    • (1997) SIAM J Numer Anal , vol.34 , Issue.6 , pp. 2228-2253
    • Chen, Z.1    Ewing, R.E.2
  • 25
    • 0036931450 scopus 로고    scopus 로고
    • Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems
    • Cockburn B., and Dawson C.N. Approximation of the velocity by coupling discontinuous Galerkin and mixed finite element methods for flow problems. Comput Geosci 6 3-4 (2002) 502-522
    • (2002) Comput Geosci , vol.6 , Issue.3-4 , pp. 502-522
    • Cockburn, B.1    Dawson, C.N.2
  • 26
    • 84966261380 scopus 로고
    • The Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 4. The multidimensional case
    • Cockburn B., Hou S.C., and Shu C.W. The Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 4. The multidimensional case. Math Comput 54 190 (1990) 545-581
    • (1990) Math Comput , vol.54 , Issue.190 , pp. 545-581
    • Cockburn, B.1    Hou, S.C.2    Shu, C.W.3
  • 27
    • 0035734429 scopus 로고    scopus 로고
    • Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids
    • Cockburn B., Kanschat G., Perugia I., and Schötzau D. Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. SIAM J Numer Anal 39 1 (2001) 264-285
    • (2001) SIAM J Numer Anal , vol.39 , Issue.1 , pp. 264-285
    • Cockburn, B.1    Kanschat, G.2    Perugia, I.3    Schötzau, D.4
  • 28
    • 1642602854 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for the Oseen equations
    • Cockburn B., Kanschat G., and Schẗzau D. The local discontinuous Galerkin method for the Oseen equations. Math Comput 73 (2003) 569-593
    • (2003) Math Comput , vol.73 , pp. 569-593
    • Cockburn, B.1    Kanschat, G.2    Schẗzau, D.3
  • 29
    • 0036556541 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for the Stokes system
    • Cockburn B., Kanschat G., Schẗzau D., and Schwab C. Local discontinuous Galerkin methods for the Stokes system. J Numer Anal 40 1 (2002) 319-343
    • (2002) J Numer Anal , vol.40 , Issue.1 , pp. 319-343
    • Cockburn, B.1    Kanschat, G.2    Schẗzau, D.3    Schwab, C.4
  • 30
    • 0002084927 scopus 로고    scopus 로고
    • The development of discontinuous Galerkin methods
    • Cockburn B., Karniadakis E., and Shu C.W. (Eds), Springer-Verlag, New York
    • Cockburn B., Karniadakis E., and Shu C.W. The development of discontinuous Galerkin methods. In: Cockburn B., Karniadakis E., and Shu C.W. (Eds). Lecture notes in computer science and engineering (2000), Springer-Verlag, New York 3-50
    • (2000) Lecture notes in computer science and engineering , pp. 3-50
    • Cockburn, B.1    Karniadakis, E.2    Shu, C.W.3
  • 31
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 3. One-dimensional systems
    • Cockburn B., Lin S.Y., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 3. One-dimensional systems. J Comput Phys 84 1 (1989) 90-113
    • (1989) J Comput Phys , vol.84 , Issue.1 , pp. 90-113
    • Cockburn, B.1    Lin, S.Y.2    Shu, C.W.3
  • 32
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 2. General framework
    • Cockburn B., and Shu C.W. TVB Runge-Kutta local projection discontinuous Galerkin finite-element method for conservation-laws. 2. General framework. Math Comput 52 186 (1989) 411-435
    • (1989) Math Comput , vol.52 , Issue.186 , pp. 411-435
    • Cockburn, B.1    Shu, C.W.2
  • 33
    • 0000869912 scopus 로고
    • The Runge-Kutta local projection rho-1-Discontinuous-Galerkin finite-element method for scalar conservation-laws
    • Cockburn B., and Shu C.W. The Runge-Kutta local projection rho-1-Discontinuous-Galerkin finite-element method for scalar conservation-laws. Rairo-Math Model Numer Anal-Model Math Anal Numer 25 3 (1991) 337-361
    • (1991) Rairo-Math Model Numer Anal-Model Math Anal Numer , vol.25 , Issue.3 , pp. 337-361
    • Cockburn, B.1    Shu, C.W.2
  • 34
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V - multidimensional systems
    • Cockburn B., and Shu C.W. The Runge-Kutta discontinuous Galerkin method for conservation laws V - multidimensional systems. J Comput Phys 141 2 (1998) 199-224
    • (1998) J Comput Phys , vol.141 , Issue.2 , pp. 199-224
    • Cockburn, B.1    Shu, C.W.2
  • 35
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • Cockburn B., and Shu C.-W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J Sci Comput 16 (2001) 173-261
    • (2001) J Sci Comput , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 36
    • 0027097662 scopus 로고
    • Continuous velocity fields and pathlines in finite element groundwater flow methods
    • Russell T.F., Ewing R.E., Brebbia C.A., Gray W.G., and Pinder G.F. (Eds), Computational Mechanics Publications, Denver
    • Cordes C., and Kinzelbach W. Continuous velocity fields and pathlines in finite element groundwater flow methods. In: Russell T.F., Ewing R.E., Brebbia C.A., Gray W.G., and Pinder G.F. (Eds). Numerical methods in water resources vol. 1 (1992), Computational Mechanics Publications, Denver 247-254
    • (1992) Numerical methods in water resources , vol.1 , pp. 247-254
    • Cordes, C.1    Kinzelbach, W.2
  • 37
    • 1642503911 scopus 로고    scopus 로고
    • k local discontinuous Galerkin method for ellipticequations
    • k local discontinuous Galerkin method for ellipticequations. SIAM J Numer Anal 40 6 (2003) 2151-2170
    • (2003) SIAM J Numer Anal , vol.40 , Issue.6 , pp. 2151-2170
    • Dawson, C.N.1
  • 38
    • 19944366692 scopus 로고    scopus 로고
    • Coupling local discontinuous and continuous Galerkin methods for flow problems
    • Dawson C.N. Coupling local discontinuous and continuous Galerkin methods for flow problems. Adv Water Resour 28 7 (2005) 729-744
    • (2005) Adv Water Resour , vol.28 , Issue.7 , pp. 729-744
    • Dawson, C.N.1
  • 39
    • 0012062665 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for convection-dominated problems
    • Discontinuous Galerkin methods. Cockburn B., Karniadakis G., and Shu C.W. (Eds), Springer-Verlag
    • Dawson C.N., Aizinger V., and Cockburn B. Local discontinuous Galerkin methods for convection-dominated problems. In: Cockburn B., Karniadakis G., and Shu C.W. (Eds). Discontinuous Galerkin methods. Theory computation and applications (2000), Springer-Verlag 309-314
    • (2000) Theory computation and applications , pp. 309-314
    • Dawson, C.N.1    Aizinger, V.2    Cockburn, B.3
  • 40
    • 0001430079 scopus 로고    scopus 로고
    • A two-grid finite difference scheme for nonlinear parabolic equations
    • Dawson C.N., Wheeler M.F., and Woodward C.S. A two-grid finite difference scheme for nonlinear parabolic equations. SIAM J Numer Anal 35 2 (1998) 435-452
    • (1998) SIAM J Numer Anal , vol.35 , Issue.2 , pp. 435-452
    • Dawson, C.N.1    Wheeler, M.F.2    Woodward, C.S.3
  • 41
    • 0028562727 scopus 로고
    • Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities
    • Durlofsky L.J. Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities. Water Resour Res 30 4 (1994) 965-973
    • (1994) Water Resour Res , vol.30 , Issue.4 , pp. 965-973
    • Durlofsky, L.J.1
  • 42
    • 0023289037 scopus 로고
    • Error estimates and automatic time step control for nonlinear parabolic problems.1
    • Eriksson K., and Johnson C. Error estimates and automatic time step control for nonlinear parabolic problems.1. SIAM J Numer Anal 24 1 (1987) 12-23
    • (1987) SIAM J Numer Anal , vol.24 , Issue.1 , pp. 12-23
    • Eriksson, K.1    Johnson, C.2
  • 43
    • 0026106415 scopus 로고
    • Adaptive finite element methods for parabolic problems, 1. A linear model problem
    • Eriksson K., and Johnson C. Adaptive finite element methods for parabolic problems, 1. A linear model problem. SIAM J Numer Anal 28 1 (1991) 43-77
    • (1991) SIAM J Numer Anal , vol.28 , Issue.1 , pp. 43-77
    • Eriksson, K.1    Johnson, C.2
  • 44
    • 67649809189 scopus 로고
    • Adaptive finite-element methods for parabolic problems. 5. Long-time integration
    • Eriksson K., and Johnson C. Adaptive finite-element methods for parabolic problems. 5. Long-time integration. SIAM J Numer Anal 32 6 (1995) 1750-1763
    • (1995) SIAM J Numer Anal , vol.32 , Issue.6 , pp. 1750-1763
    • Eriksson, K.1    Johnson, C.2
  • 45
    • 0033513105 scopus 로고    scopus 로고
    • The finite volume method for Richards equation
    • Eymard R., Gutnic M., and Hilhorst D. The finite volume method for Richards equation. Comput Geosci 3 (1999) 259-294
    • (1999) Comput Geosci , vol.3 , pp. 259-294
    • Eymard, R.1    Gutnic, M.2    Hilhorst, D.3
  • 46
    • 1342331096 scopus 로고    scopus 로고
    • Application of the discontinuous spectral Galerkin method to groundwater flow
    • Fagherazzi S., Furbish D.J., Rasetarinera P., and Hussaini M.Y. Application of the discontinuous spectral Galerkin method to groundwater flow. Adv Water Resour 27 2 (2004) 129-140
    • (2004) Adv Water Resour , vol.27 , Issue.2 , pp. 129-140
    • Fagherazzi, S.1    Furbish, D.J.2    Rasetarinera, P.3    Hussaini, M.Y.4
  • 47
    • 33846356451 scopus 로고    scopus 로고
    • Farthing MW, Kees CE, Miller CT. Mixed finite element methods and higher-order temporal approximations for variably-saturated groundwater flow. In: Water Resources Research Institute of the University of North Carolina 2002 annual conference. Raleigh, NC; 2002.
  • 48
    • 0037400206 scopus 로고    scopus 로고
    • Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow
    • Farthing M.W., Kees C.E., and Miller C.T. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv Water Resour 26 4 (2003) 373-394
    • (2003) Adv Water Resour , vol.26 , Issue.4 , pp. 373-394
    • Farthing, M.W.1    Kees, C.E.2    Miller, C.T.3
  • 49
    • 0032045989 scopus 로고    scopus 로고
    • Wetting fronts in one-dimensional periodically layered soils
    • Fennemore G., and Xin J.X. Wetting fronts in one-dimensional periodically layered soils. SIAM J Appl Math 58 2 (1998) 387-427
    • (1998) SIAM J Appl Math , vol.58 , Issue.2 , pp. 387-427
    • Fennemore, G.1    Xin, J.X.2
  • 50
    • 0029413107 scopus 로고
    • Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media
    • Forsyth P.A., Wu Y.S., and Pruess K. Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media. Adv Water Resour 18 (1995) 25-38
    • (1995) Adv Water Resour , vol.18 , pp. 25-38
    • Forsyth, P.A.1    Wu, Y.S.2    Pruess, K.3
  • 51
    • 0036998943 scopus 로고    scopus 로고
    • Estimation of internodal permeabilities for numerical simulation of unsaturated flows
    • Gasto J.M., Grifoll J., and Cohen Y. Estimation of internodal permeabilities for numerical simulation of unsaturated flows. Water Resour Res 38 12 (2002)
    • (2002) Water Resour Res , vol.38 , Issue.12
    • Gasto, J.M.1    Grifoll, J.2    Cohen, Y.3
  • 52
    • 0029542015 scopus 로고
    • One-dimensional moving-finite-element program for modeling solute transport in porous media
    • Gottardi G., and Venutelli M. One-dimensional moving-finite-element program for modeling solute transport in porous media. Comput Geosci 21 5 (1995) 663-685
    • (1995) Comput Geosci , vol.21 , Issue.5 , pp. 663-685
    • Gottardi, G.1    Venutelli, M.2
  • 53
    • 33846356089 scopus 로고    scopus 로고
    • Halt DW. A compact higher order Euler solver for unstructured grids. PhD thesis, Washington Univeristy; 1992.
  • 54
    • 24344476304 scopus 로고    scopus 로고
    • A mass-conservative switching method for simulating saturated-unsaturated flow
    • Hao X.M., Zhang R.D., and Kravchenko A. A mass-conservative switching method for simulating saturated-unsaturated flow. J Hydrol 311 1-4 (2005) 254-265
    • (2005) J Hydrol , vol.311 , Issue.1-4 , pp. 254-265
    • Hao, X.M.1    Zhang, R.D.2    Kravchenko, A.3
  • 55
    • 10444252655 scopus 로고    scopus 로고
    • A note on the design of hp-adaptive finite element methods for elliptic partial differential equations
    • Houston P., and Suli E. A note on the design of hp-adaptive finite element methods for elliptic partial differential equations. Comput Methods Appl Mech Eng 194 (2005) 229-243
    • (2005) Comput Methods Appl Mech Eng , vol.194 , pp. 229-243
    • Houston, P.1    Suli, E.2
  • 56
    • 0033617077 scopus 로고    scopus 로고
    • Multiphase flow in heterogeneous porous media: a classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach
    • Huber R., and Helmig R. Multiphase flow in heterogeneous porous media: a classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach. Int J Numer Methods Fluids 29 (1999) 899-920
    • (1999) Int J Numer Methods Fluids , vol.29 , pp. 899-920
    • Huber, R.1    Helmig, R.2
  • 57
    • 0002298440 scopus 로고
    • Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain
    • Jamet P. Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain. SIAM J Numer Anal 15 5 (1978) 1-17
    • (1978) SIAM J Numer Anal , vol.15 , Issue.5 , pp. 1-17
    • Jamet, P.1
  • 58
    • 0030953428 scopus 로고    scopus 로고
    • Mass types, element orders and solution schemes for the Richards equation
    • Ju S.H., and Kung K.J.S. Mass types, element orders and solution schemes for the Richards equation. Comput Geosci 23 2 (1997) 175-187
    • (1997) Comput Geosci , vol.23 , Issue.2 , pp. 175-187
    • Ju, S.H.1    Kung, K.J.S.2
  • 59
    • 0035366337 scopus 로고    scopus 로고
    • Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards' equation
    • Kavetski D., Binning P., and Sloan S.W. Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards' equation. Adv Water Resour 24 6 (2001) 595-605
    • (2001) Adv Water Resour , vol.24 , Issue.6 , pp. 595-605
    • Kavetski, D.1    Binning, P.2    Sloan, S.W.3
  • 60
    • 0036822365 scopus 로고    scopus 로고
    • Noniterative time stepping schemes with adaptive truncation error control for the solution of Richards' equation
    • Kavetski D., Binning P., and Sloan S.W. Noniterative time stepping schemes with adaptive truncation error control for the solution of Richards' equation. Water Resour Res 38 10 (2002)
    • (2002) Water Resour Res , vol.38 , Issue.10
    • Kavetski, D.1    Binning, P.2    Sloan, S.W.3
  • 61
    • 33846375140 scopus 로고    scopus 로고
    • Kees CE, Miller CT. Fully implicit temporal integration of index one differential-algebraic equations from nonlinear porous media flow. In: Society for industrial and applied mathematics 50th anniversary and 2002 annual meeting. Philadelphia, PA; 2002.
  • 62
    • 0032101424 scopus 로고    scopus 로고
    • Comparison of iterative methods for improved solutions of the fluid flow equation in partially saturated porous media
    • Lehmann F., and Ackerer P.H. Comparison of iterative methods for improved solutions of the fluid flow equation in partially saturated porous media. Transp Porous Media 31 3 (1998) 275-292
    • (1998) Transp Porous Media , vol.31 , Issue.3 , pp. 275-292
    • Lehmann, F.1    Ackerer, P.H.2
  • 63
    • 31644448171 scopus 로고    scopus 로고
    • A spatially and temporally adaptive solution of Richards' equation
    • Miller C.T., Abhishek C., and Farthing M.W. A spatially and temporally adaptive solution of Richards' equation. Adv Water Resour 29 4 (2005) 525-545
    • (2005) Adv Water Resour , vol.29 , Issue.4 , pp. 525-545
    • Miller, C.T.1    Abhishek, C.2    Farthing, M.W.3
  • 65
    • 77956673859 scopus 로고    scopus 로고
    • Higher order locally conservative temporal integration methods for modeling multiphase flow in porous media
    • XIV International conference on computational methods in water resources. Hassanizadeh S.M., Schotting R.J., Gray W.G., and Pinder G.F. (Eds), Elsevier, Delft, The Netherlands Volume developments in water science, vol. 47
    • Miller C.T., Farthing M.W., Kees C.E., and Kelley C.T. Higher order locally conservative temporal integration methods for modeling multiphase flow in porous media. In: Hassanizadeh S.M., Schotting R.J., Gray W.G., and Pinder G.F. (Eds). XIV International conference on computational methods in water resources. Computational methods in water resources vol. 1 (2002), Elsevier, Delft, The Netherlands 249-256 Volume developments in water science, vol. 47
    • (2002) Computational methods in water resources , vol.1 , pp. 249-256
    • Miller, C.T.1    Farthing, M.W.2    Kees, C.E.3    Kelley, C.T.4
  • 66
    • 0031689647 scopus 로고    scopus 로고
    • Robust solution of Richards' equation for non-uniform porous media
    • Miller C.T., Williams G.A., Kelley C.T., and Tocci M.D. Robust solution of Richards' equation for non-uniform porous media. Water Resour Res 34 10 (1998) 2599-2610
    • (1998) Water Resour Res , vol.34 , Issue.10 , pp. 2599-2610
    • Miller, C.T.1    Williams, G.A.2    Kelley, C.T.3    Tocci, M.D.4
  • 67
    • 0028669967 scopus 로고
    • Application of the mixed hybrid finite element approximation in a groundwater flow model: luxury or necessity?
    • Mosé R., Siegel P., and Ackerer P. Application of the mixed hybrid finite element approximation in a groundwater flow model: luxury or necessity?. Water Resour Res 30 11 (1994) 3001-3012
    • (1994) Water Resour Res , vol.30 , Issue.11 , pp. 3001-3012
    • Mosé, R.1    Siegel, P.2    Ackerer, P.3
  • 68
    • 0016961814 scopus 로고
    • A new model for predicting the hydraulic conductivity of unsaturated porous media
    • Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 12 3 (1976) 513-522
    • (1976) Water Resour Res , vol.12 , Issue.3 , pp. 513-522
    • Mualem, Y.1
  • 69
    • 0032209437 scopus 로고    scopus 로고
    • A discontinuous hp finite element method for diffusion problems
    • Oden J.T., Babuska I., and Baumann C.E. A discontinuous hp finite element method for diffusion problems. J Comput Phys 146 2 (1998) 491-519
    • (1998) J Comput Phys , vol.146 , Issue.2 , pp. 491-519
    • Oden, J.T.1    Babuska, I.2    Baumann, C.E.3
  • 70
    • 33846348023 scopus 로고    scopus 로고
    • A conservative DGM for convection-diffusion and Navier-Stokes problems
    • Cockburn B., Karniadakis G.E., and Shu C. (Eds), Springer-Verlag, Providence, RI
    • Oden T.J., and Baumann C. A conservative DGM for convection-diffusion and Navier-Stokes problems. In: Cockburn B., Karniadakis G.E., and Shu C. (Eds). Proceedings of the DGM International Symposium (1999), Springer-Verlag, Providence, RI
    • (1999) Proceedings of the DGM International Symposium
    • Oden, T.J.1    Baumann, C.2
  • 71
    • 0029782925 scopus 로고    scopus 로고
    • Finite element methods for modeling water flow in variably saturated porous media: numerical oscillation and mass-distributed schemes
    • Pan L., Warrick A.W., and Wierenga P.J. Finite element methods for modeling water flow in variably saturated porous media: numerical oscillation and mass-distributed schemes. Water Resour Res 32 6 (1996) 1883-1889
    • (1996) Water Resour Res , vol.32 , Issue.6 , pp. 1883-1889
    • Pan, L.1    Warrick, A.W.2    Wierenga, P.J.3
  • 72
    • 0028666563 scopus 로고
    • A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems
    • Paniconi C., and Putti M. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems. Water Resour Res 30 12 (1994) 3357-3374
    • (1994) Water Resour Res , vol.30 , Issue.12 , pp. 3357-3374
    • Paniconi, C.1    Putti, M.2
  • 73
    • 0041703090 scopus 로고
    • Impact of grid resolution and parametric representation on multiphase flow simulations
    • Peters A., Wittum G., Herrling B., Meissner U., Brebbia C.A., Gray W.G., and Pinder G.F. (Eds), Kluwer Academic Publishers, Heidelberg, Germany
    • Rathfelder K., and Abriola L.M. Impact of grid resolution and parametric representation on multiphase flow simulations. In: Peters A., Wittum G., Herrling B., Meissner U., Brebbia C.A., Gray W.G., and Pinder G.F. (Eds). Computational methods in water resources X vol. 2 (1994), Kluwer Academic Publishers, Heidelberg, Germany 983-990
    • (1994) Computational methods in water resources X , vol.2 , pp. 983-990
    • Rathfelder, K.1    Abriola, L.M.2
  • 74
    • 0343831462 scopus 로고    scopus 로고
    • Part II. Discontinuous Galerkin method applied to a single phase flow in porous media
    • Rivière B., Wheeler M.F., and Banas K. Part II. Discontinuous Galerkin method applied to a single phase flow in porous media. Comput Geosci 4 4 (2000) 337-349
    • (2000) Comput Geosci , vol.4 , Issue.4 , pp. 337-349
    • Rivière, B.1    Wheeler, M.F.2    Banas, K.3
  • 75
    • 0033511173 scopus 로고    scopus 로고
    • Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I
    • Rivière B., Wheeler M.F., and Girault V. Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. Part I. Comput Geosci 3 3-4 (1999) 337-360
    • (1999) Comput Geosci , vol.3 , Issue.3-4 , pp. 337-360
    • Rivière, B.1    Wheeler, M.F.2    Girault, V.3
  • 76
    • 85005502114 scopus 로고
    • Gold mining affects ground water
    • Ross C. Gold mining affects ground water. Ground Water Monit Rev 12 4 (1992) 100-102
    • (1992) Ground Water Monit Rev , vol.12 , Issue.4 , pp. 100-102
    • Ross, C.1
  • 77
    • 0025247474 scopus 로고
    • Efficient numerical methods for infiltration using Richards' equation
    • Ross P.J. Efficient numerical methods for infiltration using Richards' equation. Water Resour Res 26 2 (1990) 279-290
    • (1990) Water Resour Res , vol.26 , Issue.2 , pp. 279-290
    • Ross, P.J.1
  • 78
    • 0037383334 scopus 로고    scopus 로고
    • High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD
    • Shu C.W. High-order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD. Int J Comput Fluid Dyn 17 2 (2003) 107-118
    • (2003) Int J Comput Fluid Dyn , vol.17 , Issue.2 , pp. 107-118
    • Shu, C.W.1
  • 79
    • 1942475854 scopus 로고    scopus 로고
    • Local discontinuous Galerkin for partial differential equations with higher order derivatives
    • Shu C.W., and Yan J. Local discontinuous Galerkin for partial differential equations with higher order derivatives. J Sci Comput 17 (2002) 27-47
    • (2002) J Sci Comput , vol.17 , pp. 27-47
    • Shu, C.W.1    Yan, J.2
  • 80
    • 33846380675 scopus 로고    scopus 로고
    • Simunek J, Vogel T, Genuchten MT. The SWMS2D code for simulating water flow and solute transport in two-dimensional variably saturated media. Technical report. U.S. Salinity Laboratory, Agriculatural Research Service, U.S. Department of Agriculture; 1994.
  • 81
    • 0036989014 scopus 로고    scopus 로고
    • A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media
    • Slodicka M. A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media. SIAM J Sci Comput 23 5 (2002) 1593-1614
    • (2002) SIAM J Sci Comput , vol.23 , Issue.5 , pp. 1593-1614
    • Slodicka, M.1
  • 82
    • 0031079742 scopus 로고    scopus 로고
    • Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines
    • Tocci M.D., Kelley C.T., and Miller C.T. Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines. Adv Water Resour 20 1 (1997) 1-14
    • (1997) Adv Water Resour , vol.20 , Issue.1 , pp. 1-14
    • Tocci, M.D.1    Kelley, C.T.2    Miller, C.T.3
  • 83
    • 0032453911 scopus 로고    scopus 로고
    • Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions
    • Tocci M.D., Kelley C.T., Miller C.T., and Kees C.E. Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions. Comput Geosci 2 4 (1999) 291-309
    • (1999) Comput Geosci , vol.2 , Issue.4 , pp. 291-309
    • Tocci, M.D.1    Kelley, C.T.2    Miller, C.T.3    Kees, C.E.4
  • 84
    • 0034640964 scopus 로고    scopus 로고
    • Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation
    • van Dam J.C., and Feddes R.A. Numerical simulation of infiltration, evaporation and shallow groundwater levels with the Richards equation. Journal of hydrology 233 (2000) 72-85
    • (2000) Journal of hydrology , vol.233 , pp. 72-85
    • van Dam, J.C.1    Feddes, R.A.2
  • 85
    • 0019057216 scopus 로고
    • A closed-form equation for predicting the hydraulic conductivity of unsaturated soils
    • van Genuchten M.T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44 (1980) 892-898
    • (1980) Soil Sci Soc Am J , vol.44 , pp. 892-898
    • van Genuchten, M.T.1
  • 86
    • 0033597588 scopus 로고    scopus 로고
    • An evaluation of temporally adaptive transformation approaches for solving Richards' equation
    • Williams G.A., and Miller C.T. An evaluation of temporally adaptive transformation approaches for solving Richards' equation. Adv Water Resour 22 8 (1999) 831-840
    • (1999) Adv Water Resour , vol.22 , Issue.8 , pp. 831-840
    • Williams, G.A.1    Miller, C.T.2
  • 87
    • 0034029334 scopus 로고    scopus 로고
    • Transformation approaches for simulating flow in variably saturated porous media
    • Williams G.A., Miller C.T., and Kelley C.T. Transformation approaches for simulating flow in variably saturated porous media. Water Resour Res 36 4 (2000) 923-934
    • (2000) Water Resour Res , vol.36 , Issue.4 , pp. 923-934
    • Williams, G.A.1    Miller, C.T.2    Kelley, C.T.3
  • 88
    • 0001077416 scopus 로고    scopus 로고
    • Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media
    • Woodward C.S., and Dawson C.N. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media. SIAM J Numer Anal 37 3 (2000) 701-724
    • (2000) SIAM J Numer Anal , vol.37 , Issue.3 , pp. 701-724
    • Woodward, C.S.1    Dawson, C.N.2
  • 89
    • 0035135098 scopus 로고    scopus 로고
    • On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media
    • Wu Y.S., and Forsyth P.A. On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media. J Contam Hydrol 48 3-4 (2001) 277-304
    • (2001) J Contam Hydrol , vol.48 , Issue.3-4 , pp. 277-304
    • Wu, Y.S.1    Forsyth, P.A.2
  • 90
    • 0038693389 scopus 로고    scopus 로고
    • A local discontinuous Galerkin method for KdV type equations
    • Yan J., and Shu C.W. A local discontinuous Galerkin method for KdV type equations. SIAM J Numer Anal 40 2 (2002) 769-791
    • (2002) SIAM J Numer Anal , vol.40 , Issue.2 , pp. 769-791
    • Yan, J.1    Shu, C.W.2
  • 91
    • 0001264684 scopus 로고    scopus 로고
    • A new formulation of the mixed finite element method for solving elliptic and parabolic PDEs with triangular elements
    • Younes A., Mos R., Ackerer P., and Chavent G. A new formulation of the mixed finite element method for solving elliptic and parabolic PDEs with triangular elements. J Comput Phys (1999) 148-167
    • (1999) J Comput Phys , pp. 148-167
    • Younes, A.1    Mos, R.2    Ackerer, P.3    Chavent, G.4
  • 92
    • 0027040672 scopus 로고
    • Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils
    • Zaidel J., and Russo D. Estimation of finite difference interblock conductivities for simulation of infiltration into initially dry soils. Water Resour Res 28 9 (1992) 2285-2295
    • (1992) Water Resour Res , vol.28 , Issue.9 , pp. 2285-2295
    • Zaidel, J.1    Russo, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.