메뉴 건너뛰기




Volumn 14, Issue 6, 1998, Pages 739-780

A Family of ELLAM Schemes for Advection-Diffusion-Reaction Equations and Their Convergence Analyses

Author keywords

Advection diffusion reaction transport equations; Characteristic methods; Error estimates; Eulerian Lagrangian methods

Indexed keywords


EID: 0000598392     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199811)14:6<739::AID-NUM3>3.0.CO;2-R     Document Type: Article
Times cited : (20)

References (55)
  • 2
    • 0011994807 scopus 로고
    • The mathematics of reservoir simulation
    • SIAM, Philadelphia
    • R. E. Ewing, Ed.,The mathematics of reservoir simulation, Research Frontiers in Applied Mathematics, Vol. 1, SIAM, Philadelphia, 1984.
    • (1984) Research Frontiers in Applied Mathematics , vol.1
    • Ewing, R.E.1
  • 5
    • 0021494519 scopus 로고
    • Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems
    • J. W. Barrett and K. W. Morton, "Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems," Comp. Meth. Appl. Mech. Engrg. 45, 97-122 (1984).
    • (1984) Comp. Meth. Appl. Mech. Engrg. , vol.45 , pp. 97-122
    • Barrett, J.W.1    Morton, K.W.2
  • 6
    • 0019607241 scopus 로고
    • Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A. Brooks and T. J. R. Hughes, "Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations," Comp. Meth. Appl. Mech. Engrg. 32, 199-259 (1982).
    • (1982) Comp. Meth. Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.1    Hughes, T.J.R.2
  • 7
    • 84985370077 scopus 로고
    • A new numerical approach for the advective-diffusive transport equation
    • M. A. Celia, I. Herrera, E. T. Bouloutas, and J. S. Kindred, "A new numerical approach for the advective-diffusive transport equation," Num. Meth. PDEs 5, 203-226 (1989).
    • (1989) Num. Meth. PDEs , vol.5 , pp. 203-226
    • Celia, M.A.1    Herrera, I.2    Bouloutas, E.T.3    Kindred, J.S.4
  • 8
    • 0017220171 scopus 로고
    • Finite element methods for second order differential equations with significant first derivatives
    • I. Christie, D. F. Griffiths, A. R. Mitchell, and O. C. Zienkiewicz, "Finite element methods for second order differential equations with significant first derivatives," Int. J. Num. Engrg. 10, 1389-1396 (1976).
    • (1976) Int. J. Num. Engrg. , vol.10 , pp. 1389-1396
    • Christie, I.1    Griffiths, D.F.2    Mitchell, A.R.3    Zienkiewicz, O.C.4
  • 9
    • 0026259997 scopus 로고
    • An improved cubic Petrov-Galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains
    • E. T. Bouloutas and M. A. Celia, "An improved cubic Petrov-Galerkin method for simulation of transient advection-diffusion processes in rectangularly decomposable domains," Comp. Meth. Appl. Mech. Engrg. 91, 289-308 (1991).
    • (1991) Comp. Meth. Appl. Mech. Engrg. , vol.91 , pp. 289-308
    • Bouloutas, E.T.1    Celia, M.A.2
  • 10
    • 0024656263 scopus 로고
    • Consider higher degree Petrov-Galerkin methods for the solution of the transient convection-diffusion equation
    • J. J. Westerink and D. Shea, "Consider higher degree Petrov-Galerkin methods for the solution of the transient convection-diffusion equation," Int. J. Num. Meth. Engrg. 28, 1077-1101. (1989).
    • (1989) Int. J. Num. Meth. Engrg. , vol.28 , pp. 1077-1101
    • Westerink, J.J.1    Shea, D.2
  • 11
    • 84968481723 scopus 로고
    • Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems
    • K. Eriksson and C. Johnson, "Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems," Math. Comp. 60, 167-188 (1993).
    • (1993) Math. Comp. , vol.60 , pp. 167-188
    • Eriksson, K.1    Johnson, C.2
  • 12
    • 0013724411 scopus 로고
    • A multi-dimensional upwind scheme with no crosswind diffusion
    • T. J. R. Hughes, Ed., ASME, New York
    • T. J. R. Hughes and A. N. Brooks, "A multi-dimensional upwind scheme with no crosswind diffusion," in Finite Element Methods for Convection Dominated Flows, T. J. R. Hughes, Ed., ASME, New York, 1985, pp. 19-35.
    • (1985) Finite Element Methods for Convection Dominated Flows , pp. 19-35
    • Hughes, T.J.R.1    Brooks, A.N.2
  • 13
    • 0022807116 scopus 로고
    • A new finite element formulation for computational fluid dynamics: III. The general streamline operator for multidimensional advective-diffusive systems
    • T. J. R. Hughes and M. Mallet, "A new finite element formulation for computational fluid dynamics: III. The general streamline operator for multidimensional advective-diffusive systems," Comp. Meth. Appl. Mech. Engrg. 58, 305-328 (1986).
    • (1986) Comp. Meth. Appl. Mech. Engrg. , vol.58 , pp. 305-328
    • Hughes, T.J.R.1    Mallet, M.2
  • 14
    • 84966258545 scopus 로고
    • Crosswind smear and pointwise errors in streamline diffusion finite element methods
    • C. Johnson, A. H. Schatz, and L. B. Wahlbin, "Crosswind smear and pointwise errors in streamline diffusion finite element methods," Math. Comp. 49, 25-38 (1987).
    • (1987) Math. Comp. , vol.49 , pp. 25-38
    • Johnson, C.1    Schatz, A.H.2    Wahlbin, L.B.3
  • 15
    • 84966232205 scopus 로고
    • On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws
    • C. Johnson, A. Szepessy, and P. Hansbo, "On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws," Math. Comp. 54, 107-129 (1990).
    • (1990) Math. Comp. , vol.54 , pp. 107-129
    • Johnson, C.1    Szepessy, A.2    Hansbo, P.3
  • 16
    • 0001205207 scopus 로고
    • Stabilized finite element methods for singularly perturbed parabolic problems
    • G. Lube and D. Weiss, "Stabilized finite element methods for singularly perturbed parabolic problems," Appl. Num. Math. 17, 431-459 (1995).
    • (1995) Appl. Num. Math. , vol.17 , pp. 431-459
    • Lube, G.1    Weiss, D.2
  • 19
    • 84966238599 scopus 로고
    • An analysis of discontinuous Galerkin methods for a scalar hyperbolic equation
    • C. Johnson and J. Pitkaranta, "An analysis of discontinuous Galerkin methods for a scalar hyperbolic equation," Math. Comp. 46, 1-26 (1986).
    • (1986) Math. Comp. , vol.46 , pp. 1-26
    • Johnson, C.1    Pitkaranta, J.2
  • 20
    • 84968517725 scopus 로고
    • The discontinuous Galerkin method with diffusion
    • G. R. Richter, "The discontinuous Galerkin method with diffusion," Math. Comp. 58, 631-643. (1992).
    • (1992) Math. Comp. , vol.58 , pp. 631-643
    • Richter, G.R.1
  • 21
    • 0000480805 scopus 로고
    • A direct Eulerian MUSCL scheme for gas dynamics
    • P. Colella, "A direct Eulerian MUSCL scheme for gas dynamics," SIAM J. Sci. Stat. Comp. 6, 104-117 (1985).
    • (1985) SIAM J. Sci. Stat. Comp. , vol.6 , pp. 104-117
    • Colella, P.1
  • 22
    • 0001394094 scopus 로고
    • On Godunov-type methods for gas dynamics
    • B. Einfeldt, "On Godunov-type methods for gas dynamics," SIAM J. Num. Anal. 25, 294-318 (1988).
    • (1988) SIAM J. Num. Anal. , vol.25 , pp. 294-318
    • Einfeldt, B.1
  • 23
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially nonoscillatory schemes, III
    • A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, "Uniformly high order accurate essentially nonoscillatory schemes, III.," J. Comp. Phys. 71, 231-241 (1987).
    • (1987) J. Comp. Phys. , vol.71 , pp. 231-241
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 24
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • C. Shu and S. Osher, "Efficient implementation of essentially non-oscillatory shock capturing schemes," J. Comp. Phys. 77, 439-471 (1988).
    • (1988) J. Comp. Phys. , vol.77 , pp. 439-471
    • Shu, C.1    Osher, S.2
  • 25
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • P. K. Sweby, "High resolution schemes using flux limiters for hyperbolic conservation laws." SIAM J. Num. Anal. 21, 995-1011 (1984).
    • (1984) SIAM J. Num. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.K.1
  • 26
    • 0002187037 scopus 로고
    • On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher, and Roe
    • B. van Leer, "On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher, and Roe," SIAM J. Sci. Stat. Comp. 5, 1-20 (1984).
    • (1984) SIAM J. Sci. Stat. Comp. , vol.5 , pp. 1-20
    • Van Leer, B.1
  • 27
    • 0000647401 scopus 로고
    • Quelques difficulties des modeles numeriques en hydraulique
    • Glowinski and Lions, Eds., North-Holland
    • J. P. Benque and J. Ronat, "Quelques difficulties des modeles numeriques en hydraulique," in Computing Methods in Applied Sciences and Engineering, Glowinski and Lions, Eds., North-Holland, 1982, pp. 471-494.
    • (1982) Computing Methods in Applied Sciences and Engineering , pp. 471-494
    • Benque, J.P.1    Ronat, J.2
  • 28
    • 0001218391 scopus 로고
    • A numerical technique for calculating the transient position of the saltwater front
    • G. F. Pinder and H. H. Cooper, "A numerical technique for calculating the transient position of the saltwater front," Water Resources Research 6, 875-882 (1970).
    • (1970) Water Resources Research , vol.6 , pp. 875-882
    • Pinder, G.F.1    Cooper, H.H.2
  • 29
    • 0001116183 scopus 로고
    • Finite elements incorporating characteristics for one-dimensional diffusion-convection equation
    • E. Varoglu and W. D. L. Finn, "Finite elements incorporating characteristics for one-dimensional diffusion-convection equation," J. Comp. Phys. 34, 371-389 (1980).
    • (1980) J. Comp. Phys. , vol.34 , pp. 371-389
    • Varoglu, E.1    Finn, W.D.L.2
  • 30
    • 0001998744 scopus 로고
    • An Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids
    • S. P. Neuman, "An Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids," J. Comp. Phys. 41, 270-294 (1981).
    • (1981) J. Comp. Phys. , vol.41 , pp. 270-294
    • Neuman, S.P.1
  • 31
    • 0001338807 scopus 로고
    • On the transport-diffusion algorithm and its application to the Navier-Stokes equations
    • O. Pironneau, "On the transport-diffusion algorithm and its application to the Navier-Stokes equations," Num. Math. 38, 309-332(1982).
    • (1982) Num. Math. , vol.38 , pp. 309-332
    • Pironneau, O.1
  • 32
    • 0001235787 scopus 로고
    • Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • J. Douglas, Jr. and T. F. Russell, "Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures," SIAM J. Num. Anal. 19, 871-885 (1982).
    • (1982) SIAM J. Num. Anal. , vol.19 , pp. 871-885
    • Douglas Jr., J.1    Russell, T.F.2
  • 33
    • 84985362818 scopus 로고
    • Characteristic adaptive sub-domain methods for reservoir flow problems
    • H. K. Dahle, M. S. Espedal, R. E. Ewing, and O. Sævareid, "Characteristic adaptive sub-domain methods for reservoir flow problems," Num. Meth. PDEs 6, 279-309 (1990).
    • (1990) Num. Meth. PDEs , vol.6 , pp. 279-309
    • Dahle, H.K.1    Espedal, M.S.2    Ewing, R.E.3    Sævareid, O.4
  • 34
    • 0022797744 scopus 로고
    • Characteristic Petrov-Galerkin subdomain methods for two-phase immiscible flow
    • M. S. Espedal and R. E. Ewing, "Characteristic Petrov-Galerkin subdomain methods for two-phase immiscible flow," Comp. Meth. Appl. Mech. Engrg. 64, 113-135 (1987).
    • (1987) Comp. Meth. Appl. Mech. Engrg. , vol.64 , pp. 113-135
    • Espedal, M.S.1    Ewing, R.E.2
  • 35
    • 0001479662 scopus 로고
    • An operator-splitting method for advection-diffusion-reaction problems
    • J. R. Whiteman, Ed., Academic Press
    • M. F. Wheeler and C. N. Dawson, "An operator-splitting method for advection-diffusion-reaction problems," in MAFELAP Proceedings, Vol. 6, J. R. Whiteman, Ed., Academic Press, 1988, pp. 463-482.
    • (1988) MAFELAP Proceedings , vol.6 , pp. 463-482
    • Wheeler, M.F.1    Dawson, C.N.2
  • 36
    • 0000654496 scopus 로고
    • Stability of the Lagrangian-Galerkin method with nonexact integration
    • K. W. Morton, A. Priestley, and E. Süli, "Stability of the Lagrangian-Galerkin method with nonexact integration," RAIRO Model. Math. Anal. Num. 22, 123-151 (1988).
    • (1988) RAIRO Model. Math. Anal. Num. , vol.22 , pp. 123-151
    • Morton, K.W.1    Priestley, A.2    Süli, E.3
  • 37
    • 0025639748 scopus 로고
    • An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation
    • M. A. Celia, T. F. Russell, I. Herrera, and R. E. Ewing, "An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation," Advances in Water Resources 13, 187-206 (1990).
    • (1990) Advances in Water Resources , vol.13 , pp. 187-206
    • Celia, M.A.1    Russell, T.F.2    Herrera, I.3    Ewing, R.E.4
  • 38
    • 0000117126 scopus 로고
    • Eulerian-Lagrangian localized adjoint methods for advection-dominated problems
    • Griffiths and Watson, Eds., Longman Scientific & Technical, Harlow, United Kingdom
    • T. F. Russell, "Eulerian-Lagrangian localized adjoint methods for advection-dominated problems," in Pitmann Research Notes in Mathematics Series, Vol. 228, Griffiths and Watson, Eds., Longman Scientific & Technical, Harlow, United Kingdom, 1990, pp. 206-228. .
    • (1990) Pitmann Research Notes in Mathematics Series , vol.228 , pp. 206-228
    • Russell, T.F.1
  • 39
    • 0029656428 scopus 로고    scopus 로고
    • A finite volume Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equations in two-dimensional multi-phase flow systems
    • P. J. Binning and M. A. Celia, "A finite volume Eulerian-Lagrangian localized adjoint method for solution of the contaminant transport equations in two-dimensional multi-phase flow systems," Water Resource Research 32, 103-114 (1996).
    • (1996) Water Resource Research , vol.32 , pp. 103-114
    • Binning, P.J.1    Celia, M.A.2
  • 40
    • 0001730925 scopus 로고
    • A comparison of ELLAM formulations for simulation of reactive transport in groundwater
    • S. Wang, Ed., University of Mississippi Press
    • M. A. Celia and L. A. Ferrand, "A comparison of ELLAM formulations for simulation of reactive transport in groundwater," in Advances in Hydro-Science and Engineering, S. Wang, Ed., University of Mississippi Press, 1993, pp.1829-1836.
    • (1993) Advances in Hydro-Science and Engineering , pp. 1829-1836
    • Celia, M.A.1    Ferrand, L.A.2
  • 41
    • 0029294340 scopus 로고
    • Eulerian-Lagrangian localized adjoint methods for a nonlinear convection-diffusion equation
    • H. K. Dahle, R. E. Ewing, and T. F. Russell, "Eulerian-Lagrangian localized adjoint methods for a nonlinear convection-diffusion equation," Comp. Meth. Appl. Mech. Engrg. 122, 223-250 (1995).
    • (1995) Comp. Meth. Appl. Mech. Engrg. , vol.122 , pp. 223-250
    • Dahle, H.K.1    Ewing, R.E.2    Russell, T.F.3
  • 42
    • 0000703559 scopus 로고    scopus 로고
    • An optimal-order error estimate to Eulerian-Lagrangian localized adjoint method for variable-coefficient advection-reaction problems
    • R. E. Ewing and H. Wang, "An optimal-order error estimate to Eulerian-Lagrangian localized adjoint method for variable-coefficient advection-reaction problems," SIAM Num. Anal. 33, 318-348 (1996).
    • (1996) SIAM Num. Anal. , vol.33 , pp. 318-348
    • Ewing, R.E.1    Wang, H.2
  • 43
    • 0027789834 scopus 로고
    • A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation
    • R. W. Healy and T. F. Russell, "A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation," Water Resources Research 29, 2399-2413 (1993).
    • (1993) Water Resources Research , vol.29 , pp. 2399-2413
    • Healy, R.W.1    Russell, T.F.2
  • 44
    • 0025551715 scopus 로고
    • Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions
    • Gambolati et al., Eds., Springer-Verlag, Berlin
    • T. F. Russell and R. V. Trujillo, "Eulerian-Lagrangian localized adjoint methods with variable coefficients in multiple dimensions," in Computational Methods in Surface Hydrology, Gambolati et al., Eds., Springer-Verlag, Berlin, 1990, pp. 357-363.
    • (1990) Computational Methods in Surface Hydrology , pp. 357-363
    • Russell, T.F.1    Trujillo, R.V.2
  • 45
    • 0030265333 scopus 로고    scopus 로고
    • Eulerian-Lagrangian localized adjoint methods for systems of nonlinear advective-diffusive-reactive equations
    • J. E. Våg, H. Wang, and H. K. Dahle, "Eulerian-Lagrangian localized adjoint methods for systems of nonlinear advective-diffusive-reactive equations," Advances in Water Resources 19, 297-315 (1996).
    • (1996) Advances in Water Resources , vol.19 , pp. 297-315
    • Våg, J.E.1    Wang, H.2    Dahle, H.K.3
  • 46
    • 84985379541 scopus 로고
    • Eulerian-Lagrangian localized adjoint method for reactive transport with biodegradation
    • H. Wang, R. E. Ewing, and M. A. Celia, "Eulerian-Lagrangian localized adjoint method for reactive transport with biodegradation," Num. Meth. PDEs 11, 229-254 (1995).
    • (1995) Num. Meth. PDEs , vol.11 , pp. 229-254
    • Wang, H.1    Ewing, R.E.2    Celia, M.A.3
  • 47
    • 0029728178 scopus 로고    scopus 로고
    • An ELLAM scheme for advection-diffusion equations in multi-dimensions
    • A. A. Aldama et al., Eds., Computational Mechanics Publications, Southampton and Boston
    • H. Wang, R. C. Sharpley, and S. Man, "An ELLAM scheme for advection-diffusion equations in multi-dimensions," in Computational Methods in Water Resources XI, Vol. 2, A. A. Aldama et al., Eds., Computational Mechanics Publications, Southampton and Boston, 1996, pp. 99-106.
    • (1996) Computational Methods in Water Resources XI , vol.2 , pp. 99-106
    • Wang, H.1    Sharpley, R.C.2    Man, S.3
  • 48
    • 0027039209 scopus 로고
    • A characteristic-mixed method for contaminant transport and miscible displacement
    • T. F. Russell et al., Eds., Computational Mechanics Publications and Eisevier Applied Science, London and New York
    • T. Arbogast, A. Chilakapati, and M. F. Wheeler, "A characteristic-mixed method for contaminant transport and miscible displacement," in Computational Methods in Water Resources IX, T. F. Russell et al., Eds., Computational Mechanics Publications and Eisevier Applied Science, London and New York, 1992, pp. 77-84. .
    • (1992) Computational Methods in Water Resources IX , pp. 77-84
    • Arbogast, T.1    Chilakapati, A.2    Wheeler, M.F.3
  • 49
    • 0000439432 scopus 로고
    • A characteristic-mixed finite element method for advection-dominated transport problems
    • T. Arbogast and M. F. Wheeler, "A characteristic-mixed finite element method for advection-dominated transport problems," SMM J. Num. Anal. 32, 404-424 (1995).
    • (1995) SMM J. Num. Anal. , vol.32 , pp. 404-424
    • Arbogast, T.1    Wheeler, M.F.2
  • 50
    • 38249010068 scopus 로고
    • A characteristic-mixed method with dynamic finite element space for convection-dominated diffusion problems
    • D. Yang, "A characteristic-mixed method with dynamic finite element space for convection-dominated diffusion problems," J. Comp. Appl. Math. 43, 343-353 (1992).
    • (1992) J. Comp. Appl. Math. , vol.43 , pp. 343-353
    • Yang, D.1
  • 51
    • 0001417548 scopus 로고    scopus 로고
    • A Runge-Kutta characteristic method for first-order linear hyperbolic equations
    • H. Wang, M. Al-Lawatia, and S. A. Telyakovskiy, "A Runge-Kutta characteristic method for first-order linear hyperbolic equations," Num. Meth. PDEs 13, 617-661 (1997).
    • (1997) Num. Meth. PDEs , vol.13 , pp. 617-661
    • Wang, H.1    Al-Lawatia, M.2    Telyakovskiy, S.A.3
  • 52
    • 84920328211 scopus 로고    scopus 로고
    • An Eulerian-Lagrangian localized adjoint method for advection-dispersion equations in two dimensions and its comparison to other schemes
    • to appear
    • H. Wang, H. K. Dahle, R. E. Ewing, R. E. M. S. Espedal, R. C. Sharpley, and S. Man, "An Eulerian-Lagrangian localized adjoint method for advection-dispersion equations in two dimensions and its comparison to other schemes," SIAM J. Sci. Comp., to appear.
    • SIAM J. Sci. Comp.
    • Wang, H.1    Dahle, H.K.2    Ewing, R.E.3    Espedal, R.E.M.S.4    Sharpley, R.C.5    Man, S.6
  • 53
    • 0003271497 scopus 로고
    • Superconvergence in Galerkin finite element methods
    • Springer-Verlag, New York
    • L. B. Wahlbin, "Superconvergence in Galerkin finite element methods," Lecture Notes in Mathematics, Vol. 1605, Springer-Verlag, New York, 1995.
    • (1995) Lecture Notes in Mathematics , vol.1605
    • Wahlbin, L.B.1
  • 55
    • 0000281250 scopus 로고
    • Some improved error estimates for the modified method of characteristics
    • C. N. Dawson, T. F. Russell, and M. F. Wheeler, "Some improved error estimates for the modified method of characteristics," SIAM J. Num. Anal. 26, 1487-1512 (1989).
    • (1989) SIAM J. Num. Anal. , vol.26 , pp. 1487-1512
    • Dawson, C.N.1    Russell, T.F.2    Wheeler, M.F.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.