메뉴 건너뛰기




Volumn 9, Issue 1, 1996, Pages 75-81

Some observations on mixed methods for fully nonlinear parabolic problems in divergence form

Author keywords

Error estimates; Mixed methods; Nonlinear parabolic problems

Indexed keywords


EID: 0012960009     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/0893-9659(95)00106-9     Document Type: Article
Times cited : (20)

References (34)
  • 1
    • 0015762231 scopus 로고
    • Conforming and non-conforming finite element methods for solving the stationary Stokes equations
    • M. Crouzeix and P.-A. Raviart, Conforming and non-conforming finite element methods for solving the stationary Stokes equations, RAIRO Anal. Numér. 7 R-3, 33-76, (1973).
    • (1973) RAIRO Anal. Numér. , vol.7 , Issue.R-3 , pp. 33-76
    • Crouzeix, M.1    Raviart, P.-A.2
  • 3
    • 0001759083 scopus 로고
    • The p-version of the finite element method
    • I. Babuška, E. Katz and R. Szabo, The p-version of the finite element method, SIAM Num. Anal. 18, 515-545, (1981).
    • (1981) SIAM Num. Anal. , vol.18 , pp. 515-545
    • Babuška, I.1    Katz, E.2    Szabo, R.3
  • 5
    • 0016093926 scopus 로고
    • On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers
    • F. Brezzi, On the existence, uniqueness, and approximation of saddle point problems arising from Lagrangian multipliers, R.A.I.R.O., Anal. Numér. 2, 129-151, (1974).
    • (1974) R.A.I.R.O., Anal. Numér. , vol.2 , pp. 129-151
    • Brezzi, F.1
  • 6
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • F. Brezzi, J. Douglas, Jr. and L.D. Marini, Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47, 217-235, (1985).
    • (1985) Numer. Math. , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas J., Jr.2    Marini, L.D.3
  • 7
    • 0002714549 scopus 로고
    • Recent results on mixed finite-element methods for second-order elliptic problems
    • Edited by A.V. Balakrishnan, A.A. Dorodnitsyn and J.L. Lions, Optimization Software, New York
    • F. Brezzi, J. Douglas, Jr. and L.D. Marini, Recent results on mixed finite-element methods for second-order elliptic problems, In Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology, (Edited by A.V. Balakrishnan, A.A. Dorodnitsyn and J.L. Lions), pp. 25-43, Optimization Software, New York, (1986).
    • (1986) Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology , pp. 25-43
    • Brezzi, F.1    Douglas J., Jr.2    Marini, L.D.3
  • 8
    • 0000698561 scopus 로고
    • Stabilized mixed methods for the Stokes problem
    • F. Brezzi and J. Douglas, Jr., Stabilized mixed methods for the Stokes problem, Numer. Math. 53, 225-235, (1988).
    • (1988) Numer. Math. , vol.53 , pp. 225-235
    • Brezzi, F.1    Douglas J., Jr.2
  • 9
    • 0002329650 scopus 로고
    • The approximation of the pressure by a mixed method in the simulation of miscible displacement
    • J. Douglas, Jr., R.E. Ewing and M.F. Wheeler. The approximation of the pressure by a mixed method in the simulation of miscible displacement, R.A.I.R.O., Anal. Numér. 17, 17-33, (1983).
    • (1983) R.A.I.R.O., Anal. Numér. , vol.17 , pp. 17-33
    • Douglas J., Jr.1    Ewing, R.E.2    Wheeler, M.F.3
  • 10
    • 34250136581 scopus 로고
    • A family of higher order mixed finite elements for plane elasticity
    • D.N. Arnold, J. Douglas, Jr. and C.P. Gupta, A family of higher order mixed finite elements for plane elasticity, Numer. Math. 45, 1-22, (1984).
    • (1984) Numer. Math. , vol.45 , pp. 1-22
    • Arnold, D.N.1    Douglas J., Jr.2    Gupta, C.P.3
  • 11
    • 0000369744 scopus 로고
    • PEERS: A new mixed finite element for plane elasticity
    • D.N. Arnold, F. Brezzi and J. Douglas, Jr., PEERS: A new mixed finite element for plane elasticity, Japan J. Appl. Math. 1, 347-367, (1984).
    • (1984) Japan J. Appl. Math. , vol.1 , pp. 347-367
    • Arnold, D.N.1    Brezzi, F.2    Douglas J., Jr.3
  • 13
    • 84966242123 scopus 로고
    • Global estimates for mixed methods for second order elliptic equations
    • J. Douglas, Jr. and J.E. Roberts. Global estimates for mixed methods for second order elliptic equations, Math. Comp. 44, 39-52, (1985).
    • (1985) Math. Comp. , vol.44 , pp. 39-52
    • Douglas J., Jr.1    Roberts, J.E.2
  • 15
    • 0007013979 scopus 로고
    • p, 1 ≤ p ≤ ∞, for mixed finite element methods for linear and quasi-linear elliptic problems
    • p, 1 ≤ p ≤ ∞, for mixed finite element methods for linear and quasi-linear elliptic problems, R.A.I.R.O. Modélisation Mathématique et Analyse Numérique 22, 371-387, (1988).
    • (1988) R.A.I.R.O. Modélisation Mathématique et Analyse Numérique , vol.22 , pp. 371-387
    • Durán, R.1
  • 16
  • 17
    • 0017633213 scopus 로고
    • An analysis of the convergence of mixed finite element methods
    • M. Fortin, An analysis of the convergence of mixed finite element methods, R.A.I.R.O., Anal. Numér. 11, 341-354, (1977).
    • (1977) R.A.I.R.O., Anal. Numér. , vol.11 , pp. 341-354
    • Fortin, M.1
  • 19
    • 0001099785 scopus 로고
    • Domain decomposition and mixed finite element methods for elliptic problems
    • Edited by R. Glowinski, G. Golub, G. Meurant and J. Periaux, SIAM, Philadelphia
    • R. Glowinski and M.F. Wheeler, Domain decomposition and mixed finite element methods for elliptic problems, In Domain Decomposition Methods for Partial Differential Equations, (Edited by R. Glowinski, G. Golub, G. Meurant and J. Periaux), pp. 144-172, SIAM, Philadelphia, (1988).
    • (1988) Domain Decomposition Methods for Partial Differential Equations , pp. 144-172
    • Glowinski, R.1    Wheeler, M.F.2
  • 21
    • 84968480755 scopus 로고
    • A mixed finite element method for a strongly nonlinear second-order elliptic problem
    • to appear
    • F.A. Milner and E.-J. Park, A mixed finite element method for a strongly nonlinear second-order elliptic problem, Math. Comp. 64, (1995) (to appear).
    • (1995) Math. Comp. , vol.64
    • Milner, F.A.1    Park, E.-J.2
  • 23
    • 0012782696 scopus 로고
    • On the stability and convergence of higher order mixed finite element methods for second order elliptic problems
    • M. Suri, On the stability and convergence of higher order mixed finite element methods for second order elliptic problems, Math. Comp. 54, 1-19, (1990).
    • (1990) Math. Comp. , vol.54 , pp. 1-19
    • Suri, M.1
  • 24
    • 84966230563 scopus 로고
    • Mixed finite element methods for quasilinear second order elliptic problems
    • F.A. Milner, Mixed finite element methods for quasilinear second order elliptic problems, Math. Comp. 44, 303-320, (1985).
    • (1985) Math. Comp. , vol.44 , pp. 303-320
    • Milner, F.A.1
  • 25
    • 85030677729 scopus 로고
    • Mixed finite element methods for nonlinear second order elliptic problems
    • to appear
    • E.-J. Park, Mixed finite element methods for nonlinear second order elliptic problems, SIAM J. Numer. Anal 32, (1995) (to appear).
    • (1995) SIAM J. Numer. Anal , vol.32
    • Park, E.-J.1
  • 26
    • 0002078165 scopus 로고
    • Error estimates for some mixed finite element methods for parabolic type problems
    • C. Johnson and V. Thomée. Error estimates for some mixed finite element methods for parabolic type problems, R.A.I.R.O., Anal. Numér. 14, 41-78, (1981).
    • (1981) R.A.I.R.O., Anal. Numér. , vol.14 , pp. 41-78
    • Johnson, C.1    Thomée, V.2
  • 28
    • 0041174664 scopus 로고
    • A mixed finite element method for the Cahn-Hilliard and the Sivashinsky equations
    • F.A. Milner, A mixed finite element method for the Cahn-Hilliard and the Sivashinsky equations, Mat. Apl. Comput. 9, 31-44, (1990).
    • (1990) Mat. Apl. Comput. , vol.9 , pp. 31-44
    • Milner, F.A.1
  • 29
    • 0039395405 scopus 로고
    • Superconvergence of mixed finite elements for parabolic equations
    • M.C.J. Squeff, Superconvergence of mixed finite elements for parabolic equations, Modélisation Mathematique et Analyse Numérique 21, 327-352, (1987).
    • (1987) Modélisation Mathematique et Analyse Numérique , vol.21 , pp. 327-352
    • Squeff, M.C.J.1
  • 31
    • 0012912772 scopus 로고
    • Analysis of mixed methods for generalized Forchheimer flow in porous media
    • Center for Applied Math, Purdue University, August
    • E.-J. Park, Analysis of mixed methods for generalized Forchheimer flow in porous media, Technical Report, 241, Center for Applied Math, Purdue University, (August 1994); RAIRO Modélisation Mathématique et Analyse Numérique, (submitted).
    • (1994) Technical Report , vol.241
    • Park, E.-J.1
  • 32
    • 85029991346 scopus 로고    scopus 로고
    • submitted
    • E.-J. Park, Analysis of mixed methods for generalized Forchheimer flow in porous media, Technical Report, 241, Center for Applied Math, Purdue University, (August 1994); RAIRO Modélisation Mathématique et Analyse Numérique, (submitted).
    • RAIRO Modélisation Mathématique et Analyse Numérique
  • 34
    • 85029997962 scopus 로고    scopus 로고
    • to appear
    • E.-J. Park, Mixed methods for nonlinear second order elliptic problems in three variables, UTM, 443, Dipartimento di Matematica, Università di Trento, Trento, Italy, (1994); Numer. Methods for Partial Differential Equations (to appear).
    • Numer. Methods for Partial Differential Equations


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.