메뉴 건너뛰기




Volumn 19, Issue 3, 2003, Pages 271-283

A nonconventional Eulerian-Lagrangian single-node collocation method with hermite polynomials for unsteady-state advection-diffusion equations

Author keywords

Advection diffusion equations; Characteristic methods; Collocation method; Convection diffusion equations; Eulerian Lagrangian methods; Hermite polynomials

Indexed keywords


EID: 0037407715     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10047     Document Type: Article
Times cited : (9)

References (24)
  • 1
    • 0010639331 scopus 로고
    • A finite‐element collocation method for variably saturated flow in two space dimensions
    • 1 M. B. Allen and C. L. Murphy, A finite‐element collocation method for variably saturated flow in two space dimensions, Water Resour Res 22 (1986), 1537–1542.
    • (1986) Water Resour Res , vol.22 , pp. 1537-1542
    • Allen, M.B.1    Murphy, C.L.2
  • 2
    • 84977354567 scopus 로고
    • Hydraulics of Groundwater
    • 2 J. Bear, Hydraulics of Groundwater, New York, McGraw‐Hill, 1979.
    • (1979)
    • Bear, J.1
  • 3
    • 0000898485 scopus 로고
    • Collocation methods for parabolic partial differential equations in one space dimension
    • 3 J. H. Cerutti and S. V. Parter, Collocation methods for parabolic partial differential equations in one space dimension, Numer Math 26 (1976), 227–254.
    • (1976) Numer Math , vol.26 , pp. 227-254
    • Cerutti, J.H.1    Parter, S.V.2
  • 4
    • 84968516225 scopus 로고
    • A finite element collocation method for quasilinear parabolic equations
    • 4 J. Douglas and T. Dupont, A finite element collocation method for quasilinear parabolic equations, Math Comp 27 (1973), 17–28.
    • (1973) Math Comp , vol.27 , pp. 17-28
    • Douglas, J.1    Dupont, T.2
  • 5
    • 0035281751 scopus 로고    scopus 로고
    • Orthogonal spline collocation methods for partial differential equations, Numerical Analysis 2000, Vol. VII, Partial differential equations
    • 5 B. Bialecki and G. Fairweather, Orthogonal spline collocation methods for partial differential equations, Numerical Analysis 2000, Vol. VII, Partial differential equations, J Comput Appl Math 128 (2001), 55–82.
    • (2001) J Comput Appl Math , vol.128 , pp. 55-82
    • Bialecki, B.1    Fairweather, G.2
  • 6
    • 84985359611 scopus 로고
    • Generalized alternating‐direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems
    • 6 M. A. Celia and G. F. Pinder, Generalized alternating‐direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems, Numer Methods Partial Differential Eq 6 (1990), 215–230.
    • (1990) Numer Methods Partial Differential Eq , vol.6 , pp. 215-230
    • Celia, M.A.1    Pinder, G.F.2
  • 7
    • 0022697663 scopus 로고
    • Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables
    • 7 C. E. Greenwell‐Yanik and G. Fairweather, Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables, SIAM J Numer Anal 23 (1986), 282–296.
    • (1986) SIAM J Numer Anal , vol.23 , pp. 282-296
    • Greenwell‐Yanik, C.E.1    Fairweather, G.2
  • 8
    • 0000383666 scopus 로고
    • An C1 finite element collocation method for elliptic equations
    • 8 P. Percell and M. F. Wheeler, An C 1 finite element collocation method for elliptic equations, SIAM J Numer Anal 17 (1980), 605–622.
    • (1980) SIAM J Numer Anal , vol.17 , pp. 605-622
    • Percell, P.1    Wheeler, M.F.2
  • 9
    • 16544376185 scopus 로고    scopus 로고
    • Single‐degree freedom collocation method using Hermite polynomials
    • 9 L. Wu and G. F. Pinder, Single‐degree freedom collocation method using Hermite polynomials, Contemp Math 295 (2002), 489–499.
    • (2002) Contemp Math , vol.295 , pp. 489-499
    • Wu, L.1    Pinder, G.F.2
  • 11
    • 0003286277 scopus 로고    scopus 로고
    • A family of Eulerian‐Lagrangian localized adjoint methods for multi‐dimensional advection‐reaction equations
    • 11 H. Wang, R. E. Ewing, G. Qin, S. L. Lyons, M. Al‐Lawatia, and S. Man, A family of Eulerian‐Lagrangian localized adjoint methods for multi‐dimensional advection‐reaction equations, J Comput Phys 152 (1999), 120–163.
    • (1999) J Comput Phys , vol.152 , pp. 120-163
    • Wang, H.1    Ewing, R.E.2    Qin, G.3    Lyons, S.L.4    Al‐Lawatia, M.5    Man, S.6
  • 12
    • 0001235787 scopus 로고
    • Numerical methods for convection‐dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • 12 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 Numer Anal 19 (1982), 871–885.
    • (1982) SIAM J Numer Anal , vol.19 , pp. 871-885
    • Douglas, J.1    Russell, T.F.2
  • 13
    • 0025639748 scopus 로고
    • An Eulerian‐Lagrangian localized adjoint method for the advection‐diffusion equation
    • 13 M. A. Celia, T. F. Russell, I. Herrera, and R. E. Ewing, An Eulerian‐Lagrangian localized adjoint method for the advection‐diffusion equation, Adv Water Res 13 (1990), 187–206.
    • (1990) Adv Water Res , vol.13 , pp. 187-206
    • Celia, M.A.1    Russell, T.F.2    Herrera, I.3    Ewing, R.E.4
  • 14
    • 77957214696 scopus 로고
    • Eulerian‐Lagrangian localized methods for convection‐diffusion equations and their convergence analysis
    • 14 H. Wang, R. E. Ewing, and T. F. Russell, Eulerian‐Lagrangian localized methods for convection‐diffusion equations and their convergence analysis, IMA J Numer Anal 15 (1995), 405–459.
    • (1995) IMA J Numer Anal , vol.15 , pp. 405-459
    • Wang, H.1    Ewing, R.E.2    Russell, T.F.3
  • 15
    • 0000654496 scopus 로고
    • Stability of the Lagrangian‐Galerkin method with nonexact integration
    • 15 K. W. Morton, A. Priestley, and E. Süli, Stability of the Lagrangian‐Galerkin method with nonexact integration, RAIRO M2 AN 22 (1988), 123–151.
    • (1988) RAIRO M2 AN , vol.22 , pp. 123-151
    • Morton, K.W.1    Priestley, A.2    Süli, E.3
  • 16
    • 0000935266 scopus 로고
    • A difference scheme for numerical computation of discontinuous solutions of fluid dynamics
    • 16 S. K. Godunov, A difference scheme for numerical computation of discontinuous solutions of fluid dynamics, Mat Sb 47 (1959), 271–306.
    • (1959) Mat Sb , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 17
    • 0000480805 scopus 로고
    • A direct Eulerian MUSCL scheme for gas dynamics
    • 17 P. Colella, A direct Eulerian MUSCL scheme for gas dynamics, SIAM J Sci Stat Comput 6 (1985), 104–117.
    • (1985) SIAM J Sci Stat Comput , vol.6 , pp. 104-117
    • Colella, P.1
  • 18
    • 0000296272 scopus 로고
    • A geometric approach to high resolution TVD schemes
    • 18 J. B. Goodman and R. J. LeVeque, A geometric approach to high resolution TVD schemes, SIAM J Numer Anal 25 (1988), 268–284.
    • (1988) SIAM J Numer Anal , vol.25 , pp. 268-284
    • Goodman, J.B.1    LeVeque, R.J.2
  • 19
    • 34249988639 scopus 로고
    • Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme
    • 19 B. van Leer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second order scheme, J Comput Phys 14 (1974), 361–370.
    • (1974) J Comput Phys , vol.14 , pp. 361-370
    • van Leer, B.1
  • 20
    • 0002187037 scopus 로고
    • On the relation between the upwind‐differencing schemes of Godunov, Engquist‐Osher, and Roe
    • 20 B. van Leer, On the relation between the upwind‐differencing schemes of Godunov, Engquist‐Osher, and Roe, SIAM J Sci Stat Comput 5 (1984), 1–20.
    • (1984) SIAM J Sci Stat Comput , vol.5 , pp. 1-20
    • van Leer, B.1
  • 21
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially nonoscillatory schemes, III
    • 21 A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate essentially nonoscillatory schemes, III, J Comput Phys 71 (1987), 231–241.
    • (1987) J Comput Phys , vol.71 , pp. 231-241
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 22
    • 0023329384 scopus 로고
    • Uniformly high‐order accurate non‐oscillatory schemes, I
    • 22 A. Harten and S. Osher, Uniformly high‐order accurate non‐oscillatory schemes, I, SIAM J Numer Anal 24 (1987), 279–309.
    • (1987) SIAM J Numer Anal , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 23
    • 0000592595 scopus 로고
    • Weighted essentially nonoscillatory schemes
    • 23 X.‐D. Liu, S. Osher, and T. Chan, Weighted essentially nonoscillatory schemes, J Comput Phys 115 (1994), 200–212.
    • (1994) J Comput Phys , vol.115 , pp. 200-212
    • Liu, X.‐D.1    Osher, S.2    Chan, T.3
  • 24
    • 0000034725 scopus 로고    scopus 로고
    • Essentially non‐oscillatory (ENO) and weighted essentially non‐oscillatory (WENO) schemes for hyperbolic conservation laws, in:
    • 24 C.‐W. Shu, Essentially non‐oscillatory (ENO) and weighted essentially non‐oscillatory (WENO) schemes for hyperbolic conservation laws. A. Quarteroni, editor, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics, New York, Springer‐Verlag, Vol 1697, 1997, pp 325–432.
    • (1997) , vol.1697 , pp. 325-432
    • Shu, C.‐W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.