메뉴 건너뛰기




Volumn 32, Issue 4, 1998, Pages 479-499

Expanded mixed finite element methods for linear second-order elliptic problems, I

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0039992460     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an/1998320404791     Document Type: Article
Times cited : (101)

References (33)
  • 1
    • 84968500702 scopus 로고
    • On the implementation of mixed methods as nonconforming methods for second order elliptic problems
    • T. ARBOGAST and Z. CHEN, On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math. Comp. 64 (1995), 943-972.
    • (1995) Math. Comp. , vol.64 , pp. 943-972
    • Arbogast, T.1    Chen, Z.2
  • 2
    • 0001804939 scopus 로고
    • Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates
    • D. ARNOLD and F. BREZZI, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modèl. Math. Anal. Numér. 19 (1985), 7-32.
    • (1985) RAIRO Modèl. Math. Anal. Numér. , vol.19 , pp. 7-32
    • Arnold, D.1    Brezzi, F.2
  • 3
    • 84966214346 scopus 로고
    • A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems
    • J. BRAMBLE and J. PASCIAK, A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp. 50 (1988), 1-17.
    • (1988) Math. Comp. , vol.50 , pp. 1-17
    • Bramble, J.1    Pasciak, J.2
  • 4
    • 0003199785 scopus 로고
    • Mixed finite elements for second order elliptic problems in three variables
    • F. BREZZI, J. DOUGLAS Jr., R. DURÁN and M. FORTIN, Mixed finite elements for second order elliptic problems in three variables, Numer. Math. 51 (1987), 237-250.
    • (1987) Numer. Math. , vol.51 , pp. 237-250
    • Brezzi, F.1    Douglas J., Jr.2    Durán, R.3    Fortin, M.4
  • 6
    • 34250118577 scopus 로고
    • Two families of mixed finite elements for second order elliptic problems
    • F. BREZZI, J. DOUGLAS Jr. and L. MARINI, Two families of mixed finite elements for second order elliptic problems, Numer. Math. 47 (1985), 217-235.
    • (1985) Numer. Math. , vol.47 , pp. 217-235
    • Brezzi, F.1    Douglas J., Jr.2    Marini, L.3
  • 8
    • 0027037109 scopus 로고
    • Two-phase unsaturated flow: One dimensional simulation and air phase velocities
    • M. CELIA and P. BINNING, Two-phase unsaturated flow: one dimensional simulation and air phase velocities, Water Resources Research 28 (1992), 2819-2828.
    • (1992) Water Resources Research , vol.28 , pp. 2819-2828
    • Celia, M.1    Binning, P.2
  • 9
    • 0041030278 scopus 로고
    • Unified analysis of the hybrid form of mixed finite elements for second order elliptic problems
    • Z. CHEN, Unified analysis of the hybrid form of mixed finite elements for second order elliptic problems, J. Engng. Math. 8 (1991), 91-102.
    • (1991) J. Engng. Math. , vol.8 , pp. 91-102
    • Chen, Z.1
  • 10
    • 0002444350 scopus 로고
    • Analysis of mixed methods using conforming and nonconforming finite element methods
    • Z. CHEN, Analysis of mixed methods using conforming and nonconforming finite element methods, RAIRO Modèl. Math. Anal. Numér. 27 (1993), 9-34.
    • (1993) RAIRO Modèl. Math. Anal. Numér. , vol.27 , pp. 9-34
    • Chen, Z.1
  • 11
    • 0003343999 scopus 로고
    • p-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems
    • Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, I. Babuska et al., Springer-Verlag, Berlin and New York
    • p-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems, in Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, I. Babuska et al., eds., The IMA Volumes in Mathematics and its Applications, Springer-Verlag, Berlin and New York, 75 (1995), 187-200.
    • (1995) The IMA Volumes in Mathematics and Its Applications , vol.75 , pp. 187-200
    • Chen, Z.1
  • 12
    • 0001167127 scopus 로고
    • BDM mixed methods for a nonlinear elliptic problem
    • Z. CHEN, BDM mixed methods for a nonlinear elliptic problem, J. Comp. Appl. Math. 53 (1994), 207-223.
    • (1994) J. Comp. Appl. Math. , vol.53 , pp. 207-223
    • Chen, Z.1
  • 13
    • 85030037713 scopus 로고    scopus 로고
    • Expanded mixed finite element methods for quasilinear second order elliptic problems 11
    • IMA Preprint Series # 1278, 1994, in press
    • Z. CHEN, Expanded mixed finite element methods for quasilinear second order elliptic problems 11, IMA Preprint Series # 1278, 1994, RAIRO Modèl. Math. anal. Numér., in press.
    • RAIRO Modèl. Math. Anal. Numér.
    • Chen, Z.1
  • 14
    • 51249179041 scopus 로고
    • Prismatic mixed finite elements for second order elliptic problems
    • Z. CHEN and J. DOUGLAS Jr., Prismatic mixed finite elements for second order elliptic problems, Calcolo 26 (1989), 135-148.
    • (1989) Calcolo , vol.26 , pp. 135-148
    • Chen, Z.1    Douglas J., Jr.2
  • 17
    • 0002329650 scopus 로고
    • The approximation of the pressure by a mixed method in the simulation of miscible displacement
    • J. DOUGLAS, R. EWING and M. WHEELER, The approximation of the pressure by a mixed method in the simulation of miscible displacement, RAIRO Anal. Numér. 17 (1983), 17-33.
    • (1983) RAIRO Anal. Numér. , vol.17 , pp. 17-33
    • Douglas, J.1    Ewing, R.2    Wheeler, M.3
  • 18
    • 0001400968 scopus 로고
    • A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media
    • J. DOUGLAS Jr., R. EWING and M. WHEELER, A time-discretization procedure for a mixed finite element approximation of miscible displacement in porous media, RAIRO Anal. Numér. 17 (1983), 249-265.
    • (1983) RAIRO Anal. Numér. , vol.17 , pp. 249-265
    • Douglas J., Jr.1    Ewing, R.2    Wheeler, M.3
  • 20
    • 84966242123 scopus 로고
    • Global estimates for mixed methods for second order elliptic problems
    • J. DOUGLAS Jr. and J. ROBERTS. Global estimates for mixed methods for second order elliptic problems. Math. Comp. 45 (1985), 39-52.
    • (1985) Math. Comp. , vol.45 , pp. 39-52
    • Douglas J., Jr.1    Roberts, J.2
  • 21
    • 0001134272 scopus 로고
    • A new family of mixed finite element spaces over rectangles
    • J. DOUGLAS Jr. and J. WANG, A new family of mixed finite element spaces over rectangles, Mat. Aplic. Comput. 12 (1993), 183-197.
    • (1993) Mat. Aplic. Comput. , vol.12 , pp. 183-197
    • Douglas J., Jr.1    Wang, J.2
  • 22
    • 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, RAIRO Mod. Math. Anal. Numér. 22 (1988), 371-387.
    • (1988) RAIRO Mod. Math. Anal. Numér. , vol.22 , pp. 371-387
    • Durán, R.1
  • 23
    • 0013044931 scopus 로고
    • Preconditioning indefinite systems arising from the mixed finite element discretization of second-order elliptic systems
    • O. Axelsson and L. Kolotilina, eds., Lecture Notes in Math. 1457, Springer-Verlag, Berlin
    • R. EWING, R. LAZAROV, P. LU and P. VASSILEVSKI, Preconditioning indefinite systems arising from the mixed finite element discretization of second-order elliptic systems, in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., Lecture Notes in Math. 1457, Springer-Verlag, Berlin (1990), 28-43.
    • (1990) Preconditioned Conjugate Gradient Methods , pp. 28-43
    • Ewing, R.1    Lazarov, R.2    P, L.U.3    Vassilevski, P.4
  • 24
    • 0000266627 scopus 로고
    • A new mixed finite element method for the timoshenko beam problem
    • L. FRANCA and A. LOULA, A new mixed finite element method for the Timoshenko beam problem, RAIRO Mod. Math. Anal. Numér. 25 (1991), 561-578.
    • (1991) RAIRO Mod. Math. Anal. Numér. , vol.25 , pp. 561-578
    • Franca, L.1    Loula, A.2
  • 25
    • 0000238638 scopus 로고
    • ∞-error estimates for nonconforming and mixed finite element methods of lowest order
    • ∞-error estimates for nonconforming and mixed finite element methods of lowest order, Numer. Math. 50 (1987), 587-611.
    • (1987) Numer. Math. , vol.50 , pp. 587-611
    • Gastaldi, L.1    Nochetto, R.2
  • 29
    • 0016555955 scopus 로고
    • Solution of sparse indefinite systems of linear equations
    • C. PAIGE and M. SAUNDERS, Solution of sparse indefinite systems of linear equations, SIAM Numer. anal. 12 (1975), 617-629.
    • (1975) SIAM Numer. Anal. , vol.12 , pp. 617-629
    • Paige, C.1    Saunders, M.2
  • 30
    • 0001175293 scopus 로고
    • A mixed finite element method for second order elliptic problems
    • Springer, Berlin
    • P. A. RAVIART and J. M. THOMAS, A mixed finite element method for second order elliptic problems. Lecture Notes in Math. 606, Springer, Berlin, 1977, pp. 292-315.
    • (1977) Lecture Notes in Math. , vol.606 , pp. 292-315
    • Raviart, P.A.1    Thomas, J.M.2
  • 31
    • 0001464667 scopus 로고
    • A preconditioned iterative method for saddle-point problems
    • T. RÜSTEN and R. WINTHER, A preconditioned iterative method for saddle-point problems, SIAM J. Matrix Anal. Appl. 13 (1992), 887-904.
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , pp. 887-904
    • Rüsten, T.1    Winther, R.2
  • 32
    • 0039251736 scopus 로고
    • Postprocessing schemes for some mixed finite elements
    • R. STENBERG, Postprocessing schemes for some mixed finite elements, RAIRO Modèl. Math. Anal. Numér. 25 (1991), 151-167.
    • (1991) RAIRO Modèl. Math. Anal. Numér. , vol.25 , pp. 151-167
    • Stenberg, R.1
  • 33
    • 0023017458 scopus 로고
    • Experimental and numerical analysis of two-phase infiltration in a partially saturated soil
    • J. TOUMA and M. VAUCLIN, Experimental and numerical analysis of two-phase infiltration in a partially saturated soil, Transport in Porous Media 1 (1986), 27-55.
    • (1986) Transport in Porous Media , vol.1 , pp. 27-55
    • Touma, J.1    Vauclin, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.