메뉴 건너뛰기




Volumn 38, Issue 6, 2001, Pages 1846-1885

An ellam scheme for multidimensional advection-reaction equations and its optimal-order error estimate

Author keywords

Characteristic methods; Convergence analysis; Error estimates; Eulerian Lagrangian methods; Numerical simulation of advection reaction equations

Indexed keywords


EID: 0034580735     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999362389     Document Type: Article
Times cited : (16)

References (29)
  • 1
    • 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, Comput. Methods Appl. Mech. Engrg., 45 (1984), pp. 97-122.
    • (1984) Comput. Methods Appl. Mech. Engrg. , vol.45 , pp. 97-122
    • Barrett, J.W.1    Morton, K.W.2
  • 3
    • 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, Comput. Methods Appl. Mech. Engrg., 32 (1982), pp. 199-259.
    • (1982) Comput. Methods Appl. Mech. Engrg. , vol.32 , pp. 199-259
    • Brooks, A.1    Hughes, T.J.R.2
  • 4
    • 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, Adv. in Water Resources, 13 (1990), pp. 187-206.
    • (1990) Adv. in Water Resources , vol.13 , pp. 187-206
    • Celia, M.A.1    Russell, T.F.2    Herrera, I.3    Ewing, R.E.4
  • 5
    • 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, Internat. J. Numer. Methods Engrg., 10 (1976), pp. 1389-1396.
    • (1976) Internat. J. Numer. Methods Engrg. , vol.10 , pp. 1389-1396
    • Christie, I.1    Griffiths, D.F.2    Mitchell, A.R.3    Zienkiewicz, O.C.4
  • 7
    • 0000480805 scopus 로고
    • A direct Eulerian MUSCL scheme for gas dynamics
    • P. COLELLA, A direct Eulerian MUSCL scheme for gas dynamics, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 104-117.
    • (1985) SIAM J. Sci. Statist. Comput. , vol.6 , pp. 104-117
    • Colella, P.1
  • 8
    • 84966217981 scopus 로고
    • Monotone difference approximations for scalar conservation laws
    • M. G. CRANDALL AND A. MAJDA, Monotone difference approximations for scalar conservation laws, Math. Comp., 34 (1980), pp. 1-21.
    • (1980) Math. Comp. , vol.34 , pp. 1-21
    • Crandall, M.G.1    Majda, A.2
  • 9
    • 0042776210 scopus 로고
    • The rate of convergence of the modified method of characteristics for linear advection equation in one dimension
    • J. C. Diaz, ed., Marcel Dekker, New York
    • C. N. DAWSON, T. F. DUPONT, AND M. F. WHEELER, The rate of convergence of the modified method of characteristics for linear advection equation in one dimension, in Mathematics for Large Scale Computing, J. C. Diaz, ed., Marcel Dekker, New York, 1989, pp. 115-126.
    • (1989) Mathematics for Large Scale Computing , pp. 115-126
    • Dawson, C.N.1    Dupont, T.F.2    Wheeler, M.F.3
  • 10
    • 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. Numer. Anal., 26 (1989), pp. 1487-1512.
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1487-1512
    • Dawson, C.N.1    Russell, T.F.2    Wheeler, M.F.3
  • 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
    • 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), pp. 871-885.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas J., Jr.1    Russell, T.F.2
  • 13
    • 0011994807 scopus 로고
    • The mathematics of reservoir simulation
    • SIAM, Philadelphia
    • R. E. EWING, ED., The Mathematics of Reservoir Simulation, Frontiers Appl. Math. 1, SIAM, Philadelphia, 1984.
    • (1984) Frontiers Appl. Math. , vol.1
    • Ewing, R.E.1
  • 14
    • 0027306971 scopus 로고
    • Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis
    • R. E. EWING AND H. WANG, Eulerian-Lagrangian localized adjoint methods for linear advection or advection-reaction equations and their convergence analysis, Comput. Mech., 12 (1993), pp. 97-121.
    • (1993) Comput. Mech. , vol.12 , pp. 97-121
    • Ewing, R.E.1    Wang, H.2
  • 15
    • 0000703559 scopus 로고    scopus 로고
    • An optimal-order error estimate for Eulerian-Lagrangian localized adjoint methods for variable-coefficient advection-reaction problems
    • R. E. EWING AND H. WANG, An optimal-order error estimate for Eulerian-Lagrangian localized adjoint methods for variable-coefficient advection-reaction problems, SIAM J. Numer. Anal., 33 (1996), pp. 318-348.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 318-348
    • Ewing, R.E.1    Wang, H.2
  • 16
    • 0005645307 scopus 로고
    • A moving point method for arbitrary Peclet number multi-dimensional convection-diffusion equations
    • C. L. FARMER, A moving point method for arbitrary Peclet number multi-dimensional convection-diffusion equations, IMA J. Numer. Anal., 5 (1980), pp. 465-480.
    • (1980) IMA J. Numer. Anal. , vol.5 , pp. 465-480
    • Farmer, C.L.1
  • 17
    • 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. Comput. Phys., 71 (1987), pp. 231-241.
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-241
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 19
    • 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 (1990), pp. 107-129.
    • (1990) Math. Comp. , vol.54 , pp. 107-129
    • Johnson, C.1    Szepessy, A.2    Hansbo, P.3
  • 22
    • 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 Modél. Math. Anal. Numér., 22 (1988), pp. 123-151.
    • (1988) RAIRO Modél. Math. Anal. Numér. , vol.22 , pp. 123-151
    • Morton, K.W.1    Priestley, A.2    Süli, E.3
  • 23
    • 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, Numer. Math., 38 (1982), pp. 309-332.
    • (1982) Numer. Math. , vol.38 , pp. 309-332
    • Pironneau, O.1
  • 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. Comput. Phys., 77 (1988), pp. 439-471.
    • (1988) J. Comput. 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. Numer. Anal., 21 (1984), pp. 995-1011.
    • (1984) SIAM J. Numer. 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. Statist. Comput., 5 (1984), pp. 1-20.
    • (1984) SIAM J. Sci. Statist. Comput. , vol.5 , pp. 1-20
    • Van Leer, B.1
  • 27
    • 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. Comput. Phys., 34 (1980), pp. 371-389.
    • (1980) J. Comput. Phys. , vol.34 , pp. 371-389
    • Varoglu, E.1    Finn, W.D.L.2
  • 29
    • 0003286277 scopus 로고    scopus 로고
    • A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations
    • 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), pp. 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.