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Volumn 40, Issue 4, 2002, Pages 1491-1515

Error analysis for characteristics-based methods for degenerate parabolic problems

Author keywords

Advection Diffusion equations; Characteristics Based finite elements; Degeneracy; Error estimates

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; ERROR ANALYSIS; FINITE ELEMENT METHOD; GALERKIN METHODS;

EID: 0141645575     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614290037068X     Document Type: Article
Times cited : (36)

References (45)
  • 1
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • H. W. ALT AND S. LUCKHAUS, Quasilinear elliptic-parabolic differential equations, Math. Z., 183 (1983), pp. 311-341.
    • (1983) Math. Z. , vol.183 , pp. 311-341
    • Alt, H.W.1    Luckhaus, S.2
  • 2
    • 0000439432 scopus 로고
    • A characteristics-mixed finite element for advection-dominated transport problems
    • T. ARBOGAST AND M. F. WHEELER, A characteristics-mixed finite element for advection-dominated transport problems, SIAM J. Numer. Anal., 32 (1995), pp. 404- 424.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 404-424
    • Arbogast, T.1    Wheeler, M.F.2
  • 3
    • 0000325197 scopus 로고    scopus 로고
    • A nonlinear mixed finite element method for a degenerate parabolic equation arising inflow in porous media
    • T. ARBOGAST, M. F. WHEELER, AND N.-Y. ZHANG, A nonlinear mixed finite element method for a degenerate parabolic equation arising inflow in porous media, SIAM J. Numer. Anal., 33 (1996), pp. 1669-1687.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1669-1687
    • Arbogast, T.1    Wheeler, M.F.2    Zhang, N.-Y.3
  • 4
    • 0003004337 scopus 로고
    • On some unsteady motions of a liquid or a gas in a porous medium
    • Akad. Nauk SSSR.
    • G. I. BARENBLATT, On some unsteady motions of a liquid or a gas in a porous medium, Akad. Nauk SSSR. Prikl. Mat. Meh., 16 (1952), pp. 67-78.
    • (1952) Prikl. Mat. Meh. , vol.16 , pp. 67-78
    • Barenblatt, G.I.1
  • 5
    • 0001035419 scopus 로고    scopus 로고
    • Finite element approximation of the transport of reactive solutes in porous media. Part II. Error estimates for equilibrium adsorption processes
    • J. W. BARRETT AND P. KNABNER, Finite element approximation of the transport of reactive solutes in porous media. Part II. Error estimates for equilibrium adsorption processes, SIAM J. Numer. Anal., 34 (1997), pp. 455-479.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 455-479
    • Barrett, J.W.1    Knabner, P.2
  • 8
    • 0025639748 scopus 로고
    • An Eulerian Lagrangian localized adjoint method for the advection-diffusion equation
    • M. A. CELLO, T. F. RUSSELL, I. HERRERA, AND R. E. EWING, An Eulerian Lagrangian localized adjoint method for the advection-diffusion equation, Adv. in Water Res., 13 (1990), pp. 187-206.
    • (1990) Adv. in Water Res. , vol.13 , pp. 187-206
    • Cello, M.A.1    Russell, T.F.2    Herrera, I.3    Ewing, R.E.4
  • 9
    • 0039992460 scopus 로고    scopus 로고
    • Expanded mixed finite element methods for linear second order elliptic problems I
    • Z. CHEN, Expanded mixed finite element methods for linear second order elliptic problems I, RAIRO Modél. Math. Anal. Nambýr., 32 (1998), pp. 479-499.
    • (1998) RAIRO Modél. Math. Anal. Numér. , vol.32 , pp. 479-499
    • Chen, Z.1
  • 10
    • 0032369306 scopus 로고    scopus 로고
    • Expanded mixed finite element methods for mice second order elliptic problems II
    • Z. CHEN, Expanded mixed finite element methods for mice second order elliptic problems II, RAIRO Modél. Math. Anal. Nambýr., 32 (1998), pp. 501-520.
    • (1998) RAIRO Modél. Math. Anal. Nambýr. , vol.32 , pp. 501-520
    • Chen, Z.1
  • 11
    • 0034446298 scopus 로고    scopus 로고
    • Formulations and numerical methods of the black oil model in porous media
    • Z. CHEN, Formulations and numerical methods of the black oil model in porous media, SIAM J. Numer. Anal., 38 (2000), pp. 489-514.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 489-514
    • Chen, Z.1
  • 12
    • 0035836868 scopus 로고    scopus 로고
    • Degenerate two-phase incompressible flow I: Existence, uniqueness and regularity of a weak solution
    • Z. CHEN, Degenerate two-phase incompressible flow I: Existence, uniqueness and regularity of a weak solution, J. Differential Equations, 171 (2001), pp. 203-232.
    • (2001) J. Differential Equations , vol.171 , pp. 203-232
    • Chen, Z.1
  • 13
    • 0000761187 scopus 로고    scopus 로고
    • Fully discrete finite element analysis of multiphase flow in ground-water hydrology
    • Z. CHEN AND R. E. EWING, Fully discrete finite element analysis of multiphase flow in ground-water hydrology, SIAM J. Numer. Anal., 34 (1997), pp. 2228-2253.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2228-2253
    • Chen, Z.1    Ewing, R.E.2
  • 14
    • 0035545019 scopus 로고    scopus 로고
    • Degenerate two-phase incompressible flow III: Sharp error estimates
    • Z. CHEN AND R. EWING, Degenerate two-phase incompressible flow III: Sharp error estimates, Numer. Math., 90 (2001), pp. 215-240.
    • (2001) Numer. Math. , vol.90 , pp. 215-240
    • Chen, Z.1    Ewing, R.2
  • 15
    • 0012065010 scopus 로고    scopus 로고
    • Degenerate two-phase incompressible flow problems I: Regularization and numerical results
    • Z. CHEN AND N. L. KHLOPINA, Degenerate two-phase incompressible flow problems I: Regularization and numerical results, Commun. Appl. Anal., 5 (2001), pp. 319-334.
    • (2001) Commun. Appl. Anal. , vol.5 , pp. 319-334
    • Chen, Z.1    Khlopina, N.L.2
  • 16
    • 0141716208 scopus 로고    scopus 로고
    • Degenerate two-phase incompressible flow problems II: Error estimates
    • Z. CHEN AND N. L. KHLOPINA, Degenerate two-phase incompressible flow problems II: Error estimates, Commun. Appl. Anal., 5 (2001), pp. 503-521.
    • (2001) Commun. Appl. Anal. , vol.5 , pp. 503-521
    • Chen, Z.1    Khlopina, N.L.2
  • 17
    • 0013322859 scopus 로고    scopus 로고
    • Degenerate two-phase incompressible flow problems III: Perturbation analysis and numerical experiments
    • Z. CHEN AND N. L. KHLOPINA, Degenerate two-phase incompressible flow problems III: Perturbation analysis and numerical experiments, Electronic J. Differential Equations, 2 (1999), pp. 29-46.
    • (1999) Electronic J. Differential Equations] , vol.2 , pp. 29-46
    • Chen, Z.1    Khlopina, N.L.2
  • 19
    • 0028485504 scopus 로고
    • Characteristic-Galerkin methods for contaminant transport with non-equilibrium adsorption kinetics
    • C. N. DAWSON, C. J. VAN DUIJN, AND M. F. WHEELER, Characteristic-Galerkin methods for contaminant transport with non-equilibrium adsorption kinetics, SIAM J. Numer. Anal., 31 (1994), pp. 982-999.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 982-999
    • Dawson, C.N.1    Van Duijn, C.J.2    Wheeler, M.F.3
  • 20
    • 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
  • 21
    • 0141604491 scopus 로고
    • A survey of numerical methods for parabolic differential equations
    • F. L. Alt, ed., Academic Press, New York
    • J. DOUGLAS, JR., A survey of numerical methods for parabolic differential equations, in Advances in Computers, Vol. 2, F. L. Alt, ed., Academic Press, New York, 1961, pp. 1-54.
    • (1961) Advances in Computers , vol.2 , pp. 1-54
    • Douglas J., Jr.1
  • 22
    • 0031473997 scopus 로고    scopus 로고
    • On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs
    • J. DOUGLAS, JR., F. FURTADO, AND F. PEREIRA, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Comput. Geosci., 1 (1997), pp. 155-190.
    • (1997) Comput. Geosci. , vol.1 , pp. 155-190
    • Douglas J., Jr.1    Furtado, F.2    Pereira, F.3
  • 23
    • 0040111765 scopus 로고    scopus 로고
    • The modified method of characteristics with adjusted advection
    • J. DOUGLAS, JR., C. S. HUANG, AND F. PEREIRA, The modified method of characteristics with adjusted advection, Numer. Math., 83 (1999), pp. 353-369
    • (1999) Numer. Math. , vol.83 , pp. 353-369
    • Douglas J., Jr.1    Huang, C.S.2    Pereira, F.3
  • 24
    • 0141827548 scopus 로고    scopus 로고
    • A Locally Conservative Eulerian-Lagrangian Numerical Method and Its Application to Nonlinear Transport in Porous Media
    • Oh for Applied Mathematics, Purdue University, West Lafayette, IN
    • J. DOUGLAS, JR., F. PEREIRA, AND L. M. YEH, A Locally Conservative Eulerian-Lagrangian Numerical Method and Its Application to Nonlinear Transport in Porous Media, Technical report 324, Oh for Applied Mathematics, Purdue University, West Lafayette, IN, 1998.
    • (1998) Technical Report , vol.324
    • Douglas J., Jr.1    Pereira, F.2    Yeh, L.M.3
  • 25
    • 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
  • 26
    • 0002509466 scopus 로고
    • Solute transport in porous media with equilibrium and non-equilibrium multiple-Site adsorption: Travelling waves
    • C. J. VAN DUIJN AND P. KNABNER, Solute transport in porous media with equilibrium and non-equilibrium multiple-site adsorption: Travelling waves, J. Reine Angew. Math., 415 (1991), pp. 1-49.
    • (1991) J. Reine Angew. Math. , vol.415 , pp. 1-49
    • Van Duijn, C.J.1    Knabner, P.2
  • 27
    • 0011994807 scopus 로고
    • The Mathematics of Reservoir Simulation
    • SIAM, Philadelphia
    • R. EWING, ED., The Mathematics of Reservoir Simulation, Frontiers Appl. Math. 1, SIAM, Philadelphia, 1984.
    • (1984) Frontiers Appl. Math. , vol.1
    • Ewing, R.1
  • 28
    • 0013016185 scopus 로고
    • A priori estimates and regularization for a class of porous medium equations
    • K. FADIMBA AND R. SHARPLEY, A priori estimates and regularization for a class of porous medium equations, Nonlinear World, 2 (1995), pp. 13-41.
    • (1995) Nonlinear World , vol.2 , pp. 13-41
    • Fadimba, K.1    Sharpley, R.2
  • 32
    • 84966199242 scopus 로고
    • Error estimates for the multidimensional two-phase Stefan problem
    • J. W. JEROME AND M. ROSE, Error estimates for the multidimensional two-phase Stefan problem, Math. Comp., 39 (1982), pp. 377-414.
    • (1982) Math. Comp. , vol.39 , pp. 377-414
    • Jerome, J.W.1    Rose, M.2
  • 36
    • 0001278368 scopus 로고
    • Approximation of degenerate parabolic problems using numerical integration
    • R. H. NOCHETTO AND C. VERDI, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25 (1988), pp. 784-814.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 784-814
    • Nochetto, R.H.1    Verdi, C.2
  • 37
    • 0001607121 scopus 로고
    • Diffusion from an instantaneous point source with a concentration-dependent coefficient
    • R. E. PATTLE, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math., 12 (1959), pp. 407-409.
    • (1959) Quart. J. Mech. Appl. Math. , vol.12 , pp. 407-409
    • Pattle, R.E.1
  • 39
    • 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
  • 40
    • 84966221941 scopus 로고
    • Numerical Methods for flow through porous media I
    • M. ROSE, Numerical Methods for flow through porous media I, Math. Comp., 40 (1983), pp. 437-467.
    • (1983) Math. Comp. , vol.40 , pp. 437-467
    • Rose, M.1
  • 41
    • 0022145330 scopus 로고
    • Time stepping along characteristics with incomplete iteration for a X approximation of miscible displacement porion media
    • T. F. RUSSELL, Time stepping along characteristics with incomplete iteration for a X approximation of miscible displacement porion media, SIAM J. Numer. Anal., 22 (1985), pp. 970-1013.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 970-1013
    • Russell, T.F.1
  • 42
    • 0002650114 scopus 로고
    • Finite element and finite difference methods for continuous flows in porous media
    • The Mathematics of Reservoir Simulation, R. Ewing, ed., SIAM, Philadelphia
    • T. F. RUSSELL AND M. F. WHEELER, Finite element and finite difference methods for continuous flows in porous media, in The Mathematics of Reservoir Simulation, Frontiers Appl. Math, l, R. Ewing, ed., SIAM, Philadelphia, 1983, pp. 35-106.
    • (1983) Frontiers Appl. Math , vol.1 , pp. 35-106
    • Russell, T.F.1    Wheeler, M.F.2
  • 44
    • 0141716207 scopus 로고    scopus 로고
    • Approximation of Nuclear Contaminant Transport Through Porous Media
    • Ph.D. thesis, Center for Applied Mathematics, Purdue University, West Lafayette, IN
    • A. M. SPAGNUOLO, Approximation of Nuclear Contaminant Transport Through Porous Media, Ph.D. thesis, Technical report 319, Center for Applied Mathematics, Purdue University, West Lafayette, IN, 1998.
    • (1998) Technical Report , vol.319
    • Spagnuolo, A.M.1
  • 45
    • 77957214696 scopus 로고
    • Eulerian-Lagrangian localized adjoint methods for convection-Diffusion equations and their convergence analysis
    • H. WANG, R. E. EWING, AND T. F. RUSSELL, Eulerian-Lagrangian localized adjoint methods for convection-diffusion equations and their convergence analysis, MA J. Numer. Anal., 15 (1995), pp. 405-459.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 405-459
    • Wang, H.1    Ewing, R.E.2    Russell, T.F.3


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