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Volumn 19, Issue 2, 2003, Pages 192-210

On the mixed finite element method with Lagrange multipliers

Author keywords

Inf sup conditions; Lagrange multipliers; Mixed finite elements; Raviart Thomas spaces

Indexed keywords


EID: 0037341030     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/num.10040     Document Type: Article
Times cited : (54)

References (24)
  • 1
    • 0033422237 scopus 로고    scopus 로고
    • Formulations mixtes augmentes et applications
    • 1 B. Achchab and A. Agouzal, Formulations mixtes augmentes et applications, Math Modelling Numer Anal 33 (1999), 459–478.
    • (1999) Math Modelling Numer Anal , vol.33 , pp. 459-478
    • Achchab, B.1    Agouzal, A.2
  • 2
    • 0042657347 scopus 로고    scopus 로고
    • An extension theorem for equilibrium finite element spaces
    • 2 A. Agouzal and J.‐M. Thomas, An extension theorem for equilibrium finite element spaces, Jpn J Indust Appl Math 13 (1996), 257–266.
    • (1996) Jpn J Indust Appl Math , vol.13 , pp. 257-266
    • Agouzal, A.1    Thomas, J.‐M.2
  • 3
    • 0001476939 scopus 로고    scopus 로고
    • Mixed finite element methods on non‐matching multiblock grids
    • 3 T. Arbogast, L. C. Cowsar, M. F. Wheeler and I. Yotov, Mixed finite element methods on non‐matching multiblock grids, SIAM J Numer Anal 37 (2000), 1295–1315.
    • (2000) SIAM J Numer Anal , vol.37 , pp. 1295-1315
    • Arbogast, T.1    Cowsar, L.C.2    Wheeler, M.F.3    Yotov, I.4
  • 4
    • 0031250556 scopus 로고    scopus 로고
    • A non‐mortar mixed finite element method for elliptic problems on non‐matching multiblock grids
    • 4 T. Arbogast and I. Yotov, A non‐mortar mixed finite element method for elliptic problems on non‐matching multiblock grids, Comput Meth Appl Mech Eng 149 (1997), 255–265.
    • (1997) Comput Meth Appl Mech Eng , vol.149 , pp. 255-265
    • Arbogast, T.1    Yotov, I.2
  • 5
    • 34250459417 scopus 로고
    • The finite element method with Lagrangian multipliers
    • 5 I. Babuška, The finite element method with Lagrangian multipliers, Numer Math 20 (1973), 179–192.
    • (1973) Numer Math , vol.20 , pp. 179-192
    • Babuška, I.1
  • 6
    • 0003444735 scopus 로고
    • Survey lectures on the mathematical foundations of the finite element method, in: The mathematical foundations of the finite element method with applications to partial differential equations
    • 6 I. Babuška and A. K. Aziz, Survey lectures on the mathematical foundations of the finite element method, A. K. Aziz, editor, The mathematical foundations of the finite element method with applications to partial differential equations, Academic Press, New York, 1972.
    • (1972)
    • Babuška, I.1    Aziz, A.K.2
  • 7
    • 0025886026 scopus 로고
    • The finite element method with Lagrange multipliers on the boundary: circumventing the Babuška‐Brezzi condition
    • 7 H. J. C. Barbosa and T. J. R. Hughes, The finite element method with Lagrange multipliers on the boundary: circumventing the Babuška‐Brezzi condition, Comput Meth Appl Mech Eng 85 (1991), 109–128.
    • (1991) Comput Meth Appl Mech Eng , vol.85 , pp. 109-128
    • Barbosa, H.J.C.1    Hughes, T.J.R.2
  • 8
    • 0002423829 scopus 로고
    • Boundary Lagrange multipliers in finite element methods: error analysis in natural norms
    • 8 H. J. C. Barbosa and T. J. R. Hughes, Boundary Lagrange multipliers in finite element methods: error analysis in natural norms, Numer Math 62 (1992), 1–15.
    • (1992) Numer Math , vol.62 , pp. 1-15
    • Barbosa, H.J.C.1    Hughes, T.J.R.2
  • 9
    • 0006629182 scopus 로고    scopus 로고
    • Analysis of new augmented Lagrangian formulations for mixed finite element schemes
    • 9 D. Boffi and C. Lovadina, Analysis of new augmented Lagrangian formulations for mixed finite element schemes, Numer Math 75 (1997), 405–419.
    • (1997) Numer Math , vol.75 , pp. 405-419
    • Boffi, D.1    Lovadina, C.2
  • 10
    • 0345908352 scopus 로고    scopus 로고
    • Remarks on augmented Lagrangian formulations for mixed finite element schemes
    • 10 D. Boffi and C. Lovadina, Remarks on augmented Lagrangian formulations for mixed finite element schemes, Unione Matematica Italiana. Bollettino A (Serie VII), 11 (1997), 41–55.
    • (1997) Unione Matematica Italiana. Bollettino A , vol.VII , Issue.11 , pp. 41-55
    • Boffi, D.1    Lovadina, C.2
  • 11
    • 0004618711 scopus 로고
    • A mixed‐Lagrange multiplier finite element method for the polyharmonic equation
    • 11 J. H. Bramble and R. S. Falk, A mixed‐Lagrange multiplier finite element method for the polyharmonic equation, RAIRO Modélisation Mathématique et Analyse Numérique, 19 (1985), 519–557.
    • (1985) RAIRO Modélisation Mathématique et Analyse Numérique , vol.19 , pp. 519-557
    • Bramble, J.H.1    Falk, R.S.2
  • 12
    • 0003881705 scopus 로고
    • Mixed and Hybrid Finite Element Methods
    • 12 F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer‐Verlag, New York, 1991.
    • (1991)
    • Brezzi, F.1    Fortin, M.2
  • 13
    • 0004088932 scopus 로고
    • Monographs and Studies in Mathematics
    • 13 P. Grisvard, Elliptic Problems in Non‐Smooth Domains, Monographs and Studies in Mathematics, 24, Pitman, London, 1985.
    • (1985) , vol.24
    • Grisvard, P.1
  • 15
    • 0029706640 scopus 로고    scopus 로고
    • Multilevel preconditioned augmented Lagrangian techniques for 2nd order mixed problems
    • 15 R. Hiptmair, T. Schiekofer, and B. Wohlmuth, Multilevel preconditioned augmented Lagrangian techniques for 2nd order mixed problems, Computing 57 (1996), 25–48.
    • (1996) Computing , vol.57 , pp. 25-48
    • Hiptmair, R.1    Schiekofer, T.2    Wohlmuth, B.3
  • 16
    • 0003668851 scopus 로고
    • Linear Partial Differential Operators
    • 16 L. Hörmander, Linear Partial Differential Operators, Springer‐Verlag, Berlin, Heidelberg, New York, 1963.
    • (1963)
    • Hörmander, L.1
  • 17
    • 85120595686 scopus 로고
    • A Lagrange‐multiplier finite element method for the stationary Stokes problems
    • 17 J. S. Jiang, A Lagrange‐multiplier finite element method for the stationary Stokes problems, Proceedings of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, Science Press, Beijing, 1985, 230–236.
    • (1985) , pp. 230-236
    • Jiang, J.S.1
  • 18
    • 85120591138 scopus 로고
    • 18 J. L. Lions and E. Magenes, Non‐Homogeneous Boundary Value Problems and Applications, vol. I, Springer‐Verlag, Berlin, Heidelberg, New York, 1972.
    • (1972) , vol.I
    • Lions, J.L.1    Magenes, E.2
  • 19
    • 0000000523 scopus 로고
    • Boundary subspaces for the finite element method with Lagrange multipliers
    • 19 J. Pitkäranta, Boundary subspaces for the finite element method with Lagrange multipliers, Numer Mathe 33 (1979), 273–289.
    • (1979) Numer Mathe , vol.33 , pp. 273-289
    • Pitkäranta, J.1
  • 20
    • 84966256931 scopus 로고
    • Local stability conditions for the Babuška method of Lagrange multipliers
    • 20 J. Pitkäranta, Local stability conditions for the Babuška method of Lagrange multipliers, Math Comput 35 (1980), 1113–1129.
    • (1980) Math Comput , vol.35 , pp. 1113-1129
    • Pitkäranta, J.1
  • 21
    • 70350643826 scopus 로고
    • A conforming finite element method with Lagrange multipliers for the biharmonic problem
    • 21 J. Pitkäranta, A conforming finite element method with Lagrange multipliers for the biharmonic problem, RAIRO Modélisation Mathématique et Analyse Numérique, 14 (1980), 309–324.
    • (1980) RAIRO Modélisation Mathématique et Analyse Numérique , vol.14 , pp. 309-324
    • Pitkäranta, J.1
  • 22
    • 84966230973 scopus 로고
    • The finite element method with Lagrange multipliers for domains with corners
    • 22 J. Pitkäranta, The finite element method with Lagrange multipliers for domains with corners, Math Comput 37 (1981), 13–30.
    • (1981) Math Comput , vol.37 , pp. 13-30
    • Pitkäranta, J.1
  • 23
    • 70350630547 scopus 로고
    • Handbook of numerical analysis
    • 23 J. E. Roberts and J.‐M. Thomas, Mixed and hybrid methods, P. G. Ciarlet and J. L. Lions, editors, Handbook of numerical analysis, vol. II, Finite element methods (Part 1), North‐Holland, Amsterdam, 1991.
    • (1991) , vol.II
    • Roberts, J.E.1    Thomas, J.‐M.2
  • 24
    • 0003435740 scopus 로고    scopus 로고
    • Mixed finite element methods for flow in porous media
    • 24 I. Yotov, Mixed finite element methods for flow in porous media, Ph.D. Thesis, Rice University, 1996.
    • (1996)
    • Yotov, I.1


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