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Volumn 63, Issue 1-2, 1996, Pages 39-75

Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems

Author keywords

Boundary elements; Constrained variational problems; Domain decomposition; Inf sup conditions; Mixed finite elements; Monotone operators

Indexed keywords


EID: 0002980012     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819608840495     Document Type: Article
Times cited : (54)

References (63)
  • 2
    • 0026928450 scopus 로고
    • Unified symmetric finite element and boundary integral variational coupling methods for linear fluid-structure interaction
    • Bielak, J., MacCamy, R.C., and Zeng, X., 1992. Unified symmetric finite element and boundary integral variational coupling methods for linear fluid-structure interaction. Numerical Methods for Partial Differential Equations, 8: 451–467.
    • (1992) Numerical Methods for Partial Differential Equations , vol.8 , pp. 451-467
    • Bielak, J.1    MacCamy, R.C.2    Zeng, X.3
  • 4
    • 0016093926 scopus 로고
    • On the existence, uniqueness and approximation of saddle point problems arising from lagrangian multipliers
    • Brezzi, F., 1974. On the existence, uniqueness and approximation of saddle point problems arising from lagrangian multipliers. RAIRO Anal. Numer., 8: 129–151.
    • (1974) RAIRO Anal. Numer. , vol.8 , pp. 129-151
    • Brezzi, F.1
  • 6
    • 51249185923 scopus 로고
    • On the coupling of boundary integral and finite element methods
    • Brezzi, F., and Johnson, C., 1979. On the coupling of boundary integral and finite element methods. Calcolo, 16: 189–201.
    • (1979) Calcolo , vol.16 , pp. 189-201
    • Brezzi, F.1    Johnson, C.2
  • 8
    • 0012565987 scopus 로고
    • Some further works on the combination of hybrid/mixed finite elements to boundary elements
    • Tanaka M., (ed), Oxford: Pergamon Press, and,. Edited by
    • Cen, Z., and Du, Q., 1987. “ Some further works on the combination of hybrid/mixed finite elements to boundary elements ”. In In Theory and Application of Boundary Element Methods, Edited by: Tanaka, M., 5–14. Oxford: Pergamon Press.
    • (1987) In Theory and Application of Boundary Element Methods , pp. 5-14
    • Cen, Z.1    Du, Q.2
  • 9
    • 0040568892 scopus 로고
    • On some coupled problems in mechanics by the coupline technique of boundary element and finite element
    • Brebbia C.A., (ed), Berlin: Springer-Verlag, and,. Edited by
    • Cen, Z., Du, Q., and Yao, Z., 1987. “ On some coupled problems in mechanics by the coupline technique of boundary element and finite element ”. In In Boundary Elements IX, Edited by: Brebbia, C.A., Vol. 1, 421–434. Berlin: Springer-Verlag.
    • (1987) In Boundary Elements IX , vol.1 , pp. 421-434
    • Cen, Z.1    Du, Q.2    Yao, Z.3
  • 10
    • 0000599701 scopus 로고
    • Symmetric methods for the coupling of finite elements and boundary elements
    • Brebbia C.A., (ed), Berlin: Springer-Verlag,. Edited by
    • Costabel, M., 1987. “ Symmetric methods for the coupling of finite elements and boundary elements ”. In In Boundary Elements IX, Edited by: Brebbia, C.A., Vol. 1, 411–420. Berlin: Springer-Verlag.
    • (1987) In Boundary Elements IX , vol.1 , pp. 411-420
    • Costabel, M.1
  • 11
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: Elementary results
    • Costabel, M., 1988. Boundary integral operators on Lipschitz domains: Elementary results. SIAM Journal on Mathematical Analysis, 19: 613–626.
    • (1988) SIAM Journal on Mathematical Analysis , vol.19 , pp. 613-626
    • Costabel, M.1
  • 12
    • 0013690223 scopus 로고
    • On the coupling of finite and boundary element methods
    • Karasözen B., (ed), Ankara: METU,. Edited by
    • Costabel, M., 1989. “ On the coupling of finite and boundary element methods ”. In In Proceedings of the International Symposium on Numerical Analysis, Edited by: Karasözen, B., 1–14. Ankara: METU.
    • (1989) In Proceedings of the International Symposium on Numerical Analysis , pp. 1-14
    • Costabel, M.1
  • 14
    • 0346173639 scopus 로고
    • Coupling of finite elements and boundary elements for transmisson problems of elastic waves
    • Cruse T.A., (ed), Berlin: Springer-Verlag, Newyork, and,. Edited by
    • Costabel, M., and Stephan, E.P., 1988. “ Coupling of finite elements and boundary elements for transmisson problems of elastic waves ”. In In IUTAM Symposium on Advanced Boundary Element Methods, Edited by: Cruse, T.A., 117–124. Berlin: Springer-Verlag. Newyork
    • (1988) In IUTAM Symposium on Advanced Boundary Element Methods , pp. 117-124
    • Costabel, M.1    Stephan, E.P.2
  • 15
    • 0025505601 scopus 로고
    • Coupling of finite and boundary element methods for an elasto-plastic interface problem
    • Costabel, M., and Stephan, E.P., 1990. Coupling of finite and boundary element methods for an elasto-plastic interface problem. SIAM Journal on Numerical Analysis, 27 (5): 1212–1226.
    • (1990) SIAM Journal on Numerical Analysis , vol.27 , Issue.5 , pp. 1212-1226
    • Costabel, M.1    Stephan, E.P.2
  • 17
    • 0001957867 scopus 로고
    • Finite element method and natural boundary reduction
    • Warsaw: Polish Academy of Sciences
    • Feng, K., 1983. “ Finite element method and natural boundary reduction ”. In In Proc. Inter. Congress of Mathematics, 1439–1453. Warsaw: Polish Academy of Sciences.
    • (1983) In Proc. Inter. Congress of Mathematics , pp. 1439-1453
    • Feng, K.1
  • 18
    • 0004773330 scopus 로고
    • The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem
    • Gatica, G.N., and Hsiao, G.C., 1989. The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem. Zeitschrift fur Analysis und ihre Anwendungen (ZAA), 8 (4): 377–387.
    • (1989) Zeitschrift fur Analysis und ihre Anwendungen (ZAA) , vol.8 , Issue.4 , pp. 377-387
    • Gatica, G.N.1    Hsiao, G.C.2
  • 19
    • 0002581406 scopus 로고
    • On a class of variational formulations for some nonlinear interface problems
    • Gatica, G.N., and Hsiao, G.C., 1990. On a class of variational formulations for some nonlinear interface problems. Rendiconti di Matematica e delle sue Applicazione, 10 (4): 681–715.
    • (1990) Rendiconti di Matematica e delle sue Applicazione , vol.10 , Issue.4 , pp. 681-715
    • Gatica, G.N.1    Hsiao, G.C.2
  • 21
    • 0006071251 scopus 로고
    • The coupling of boundary integral and finite element methods for nonmonotone nonlinear problems
    • Gatica, G.N., and Hsiao, G.C., 1992. The coupling of boundary integral and finite element methods for nonmonotone nonlinear problems. Numerical Functional analysis and Optimization, 13 (5&6): 431–447.
    • (1992) Numerical Functional analysis and Optimization , vol.13 , Issue.5-6 , pp. 431-447
    • Gatica, G.N.1    Hsiao, G.C.2
  • 22
    • 0001268829 scopus 로고
    • The uncoupling of boundary integral and finite element methods for nonlinear boundary value problems
    • G.N. and Hsiao, G.C., 1995. The uncoupling of boundary integral and finite element methods for nonlinear boundary value problems. Journal of Mathematical Analysis and Applications, 189 (5&6): 442–461.
    • (1995) Journal of Mathematical Analysis and Applications , vol.189 , Issue.5-6 , pp. 442-461
    • Hsiao, G.C.1
  • 23
    • 0003507785 scopus 로고
    • Finite Element Approximation of the Navier-Stokes Equations
    • Berlin: Springer-Verlag, Heidelberg, New York, and,. In
    • Girault, V., and Raviart, P.A., 1979. “ Finite Element Approximation of the Navier-Stokes Equations ”. In Lecture Notes in Mathematics, Vol. 749, Berlin: Springer-Verlag. Heidelberg, New York
    • (1979) Lecture Notes in Mathematics , vol.749
    • Girault, V.1    Raviart, P.A.2
  • 24
    • 0003507785 scopus 로고
    • Finite Element Methods for Navier-Stokes Equations
    • Berlin: Springer-verlag, and,. In
    • Girault, V., and Raviart, P.A., 1986. “ Finite Element Methods for Navier-Stokes Equations ”. In Theory and Algorithms, Berlin: Springer-verlag.
    • (1986) Theory and Algorithms
    • Girault, V.1    Raviart, P.A.2
  • 25
    • 0000599701 scopus 로고
    • On simplified hybrid methods for coupling of finite elements and boundary elements
    • Brebbia C.A., (ed), Berlin: Springer-Verlag,. Edited by
    • Grannell, J.J., 1987. “ On simplified hybrid methods for coupling of finite elements and boundary elements ”. In In Boundary Elements IX, Edited by: Brebbia, C.A., Vol. 1, 447–460. Berlin: Springer-Verlag.
    • (1987) In Boundary Elements IX , vol.1 , pp. 447-460
    • Grannell, J.J.1
  • 26
    • 0023329923 scopus 로고
    • On the coupling of boundary integral and finite element methods for the exterior Stokes problem in 3-D
    • Guirguis, G., 1987. On the coupling of boundary integral and finite element methods for the exterior Stokes problem in 3-D. SIAM Journal on Numerical Analysis, 24 (2): 310–322.
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , Issue.2 , pp. 310-322
    • Guirguis, G.1
  • 27
    • 0001106057 scopus 로고
    • A new class ofvariational formulations for the coupling of finite and boundary element methods
    • Han, H., 1990. A new class ofvariational formulations for the coupling of finite and boundary element methods. Journal of Computational Mathematics, 8 (3): 223–232.
    • (1990) Journal of Computational Mathematics , vol.8 , Issue.3 , pp. 223-232
    • Han, H.1
  • 28
    • 38249001383 scopus 로고
    • Nonlinear field calculations with multigrid-Newton methods
    • Heise, B., 1993. Nonlinear field calculations with multigrid-Newton methods. Impact of Computing in Science and Engineering, 5 (3): 75–110.
    • (1993) Impact of Computing in Science and Engineering , vol.5 , Issue.3 , pp. 75-110
    • Heise, B.1
  • 29
    • 0028444669 scopus 로고
    • Analysis of a fully discrete finite element method for a nonlinear magnetic field problem
    • Heise, B., 1994. Analysis of a fully discrete finite element method for a nonlinear magnetic field problem. SIAM Journal on Numerical Analysis, 31 (3): 745–759.
    • (1994) SIAM Journal on Numerical Analysis , vol.31 , Issue.3 , pp. 745-759
    • Heise, B.1
  • 30
    • 0003734307 scopus 로고
    • Finite element bending analysis for plates
    • Herrmann, L.R., 1967. Finite element bending analysis for plates. J. Eng. Mech. Div. ASCE, 93 (5): 13–26.
    • (1967) J. Eng. Mech. Div. ASCE , vol.93 , Issue.5 , pp. 13-26
    • Herrmann, L.R.1
  • 32
    • 0013650116 scopus 로고
    • The coupling of BEM and FEM - a brief review
    • Brebbia C.A., (ed), Berlin: Springer-Verlag,. Edited by
    • Hsiao, G.C., 1988. “ The coupling of BEM and FEM - a brief review ”. In In Boundary Elements X, Edited by: Brebbia, C.A., 431–445. Berlin: Springer-Verlag.
    • (1988) In Boundary Elements X , pp. 431-445
    • Hsiao, G.C.1
  • 33
    • 0000994280 scopus 로고
    • The coupling of boundary element and finite element methods. A plenary lecture at the GAMM-Tagung 1989
    • Hsiao, G.C., 1990. The coupling of boundary element and finite element methods. A plenary lecture at the GAMM-Tagung 1989. Zeitschrift fur Angewandte Mathematik und Mechanics (ZAMM), 70 (6): 493–503.
    • (1990) Zeitschrift fur Angewandte Mathematik und Mechanics (ZAMM) , vol.70 , Issue.6 , pp. 493-503
    • Hsiao, G.C.1
  • 36
    • 85012606784 scopus 로고
    • On variational formulations of boundary value problems for fluid-solid interactions
    • McCarthy M.F., Hayes M.A., (eds), Amsterdam: North-Holland, and,. Edited by
    • Hsiao, G.C., Kleinman, R.E., and Schultz, L.S., 1989. “ On variational formulations of boundary value problems for fluid-solid interactions ”. In In Elastic Wave Propagation. IUTAM Symposium on Elastic Wave Propagation, Edited by: McCarthy, M.F., and Hayes, M.A., 321–326. Amsterdam: North-Holland.
    • (1989) In Elastic Wave Propagation. IUTAM Symposium on Elastic Wave Propagation , pp. 321-326
    • Hsiao, G.C.1    Kleinman, R.E.2    Schultz, L.S.3
  • 37
    • 58149515768 scopus 로고
    • A hybrid method for an exterior boundary value problem based on asymptotic expansion, boundary integral equation and finite element approximations
    • Brebbia C.A., (ed), Berlin: Springer-Verlag, and,. Edited by
    • Hsiao, G.C., and Porter, J.F., 1986. “ A hybrid method for an exterior boundary value problem based on asymptotic expansion, boundary integral equation and finite element approximations ”. In In Innovative Numerical Mathods in Engineering, Edited by: Brebbia, C.A., 83–88. Berlin: Springer-Verlag.
    • (1986) In Innovative Numerical Mathods in Engineering , pp. 83-88
    • Hsiao, G.C.1    Porter, J.F.2
  • 38
    • 84972810525 scopus 로고
    • The coupling of BEM and FEM for the two-dimensional viscous flow problem
    • Hsiao, G.C., and Porter, J.F., 1988. The coupling of BEM and FEM for the two-dimensional viscous flow problem. Applicabl Analysis, 27: 79–108.
    • (1988) Applicabl Analysis , vol.27 , pp. 79-108
    • Hsiao, G.C.1    Porter, J.F.2
  • 40
    • 84966247121 scopus 로고
    • On the coupling of boundary integral and finite element methods
    • Johnson, C., and Nedelec, J.C., 1980. On the coupling of boundary integral and finite element methods. Mathematics of Computation, 35: 1063–1079.
    • (1980) Mathematics of Computation , vol.35 , pp. 1063-1079
    • Johnson, C.1    Nedelec, J.C.2
  • 42
    • 84961480160 scopus 로고
    • Domain decomposition methods for magnetostatic nonlinear problems in combined formulation
    • Khoromskij, B.N., Mazurkevich, G.E., and Zhidkov, E.P., 1990. Domain decomposition methods for magnetostatic nonlinear problems in combined formulation. Sov. J. Numer. Anal. Mat. Modelling, 5: 111–136.
    • (1990) Sov. J. Numer. Anal. Mat. Modelling , vol.5 , pp. 111-136
    • Khoromskij, B.N.1    Mazurkevich, G.E.2    Zhidkov, E.P.3
  • 43
    • 0000441803 scopus 로고
    • Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition. In Contemporary Mathematics
    • Quarteroni A., (ed), Providence, Rhode Island: American Mathematical Society,. Edited by
    • Langer, U., 1994. “ Parallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition. In Contemporary Mathematics ”. In Domain Decomposition Methods in Science and Engineering, Edited by: Quarteroni, A., Vol. 157, 335–344. Providence, Rhode Island: American Mathematical Society.
    • (1994) Domain Decomposition Methods in Science and Engineering , vol.157 , pp. 335-344
    • Langer, U.1
  • 48
    • 0344336416 scopus 로고
    • A symmetric definite BEM formulation for the elasto-plastic rate problem
    • Brebbia C.A., (ed), Berlin: Springer-Verlag,. Edited by
    • Polizzotto, C., 1987. “ A symmetric definite BEM formulation for the elasto-plastic rate problem ”. In In Boundary Elements IX, Edited by: Brebbia, C.A., Vol. 2, 315–334. Berlin: Springer-Verlag.
    • (1987) In Boundary Elements IX , vol.2 , pp. 315-334
    • Polizzotto, C.1
  • 49
    • 0345198977 scopus 로고
    • A consistent formulation of the BEM within elasto-plasticity
    • Cruse T.A., (ed), Berlin: Springer-Verlag,. Edited by
    • Pilizzotto, C., 1988. “ A consistent formulation of the BEM within elasto-plasticity ”. In In Advanced Boundary Elements Methods, Edited by: Cruse, T.A., 315–324. Berlin: Springer-Verlag.
    • (1988) In Advanced Boundary Elements Methods , pp. 315-324
    • Pilizzotto, C.1
  • 51
    • 84972813591 scopus 로고
    • On the Coupling of Boundary Integral and Finite Element Methods for a Class of Singular Perturbation Problems
    • 1986, University of Delaware
    • Porter, J.F., 1986. On the Coupling of Boundary Integral and Finite Element Methods for a Class of Singular Perturbation Problems. Ph.D. Dissertation. 1986, University of Delaware.
    • (1986) Ph.D. Dissertation
    • Porter, J.F.1
  • 52
    • 70350630547 scopus 로고
    • Mixed and Hybrid Methods
    • Ciarlet P.G., Lions J.L., (eds), Amsterdam: North-Holland, Finite Element Methods (Part 1), and,. Edited by
    • Roberts, J.E., and Thomas, J.M., 1989. “ Mixed and Hybrid Methods ”. In In Handbook of Numerical Analysis, Edited by: Ciarlet, P.G., and Lions, J.L., Vol. II, Amsterdam: North-Holland. Finite Element Methods (Part 1)
    • (1989) In Handbook of Numerical Analysis , vol.2
    • Roberts, J.E.1    Thomas, J.M.2
  • 54
    • 0020907857 scopus 로고
    • The coupling of boudary integral and finite element methods for the bidimensional exterior steady Stokes problem
    • Sequeira, A., 1983. The coupling of boudary integral and finite element methods for the bidimensional exterior steady Stokes problem. Mathematical Methods in the Applied Sciences, 5: 356–375.
    • (1983) Mathematical Methods in the Applied Sciences , vol.5 , pp. 356-375
    • Sequeira, A.1
  • 55
    • 0022507702 scopus 로고
    • On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady Stokes problem
    • Sequeira, A., 1986. On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady Stokes problem. Mathematical Methods in the Applied Sciences, 8: 117–133.
    • (1986) Mathematical Methods in the Applied Sciences , vol.8 , pp. 117-133
    • Sequeira, A.1
  • 56
    • 0018708763 scopus 로고
    • General stress analysis by means of integral equations and boundary elements
    • Sirtori, S., 1979. General stress analysis by means of integral equations and boundary elements. Meccanica, 14: 216–218.
    • (1979) Meccanica , vol.14 , pp. 216-218
    • Sirtori, S.1
  • 57
    • 0026982004 scopus 로고
    • Coupling of finite elements and boundary elements for some nonlinear interface problems
    • Stephan, E.P., 1992. Coupling of finite elements and boundary elements for some nonlinear interface problems. Computer Methods in Applied Mechanics and Engineering, 101: 61–72.
    • (1992) Computer Methods in Applied Mechanics and Engineering , vol.101 , pp. 61-72
    • Stephan, E.P.1
  • 59
    • 2442664654 scopus 로고
    • On asymptotic error estimates for the combined BEM and FEM
    • Shaw R.P., (ed), Springer-Verlag,. Edited by
    • Wendland, W.L., 1986. “ On asymptotic error estimates for the combined BEM and FEM ”. In In Innovative Numerical Methods in Engineering, Edited by: Shaw, R.P., 55–70. Springer-Verlag.
    • (1986) In Innovative Numerical Methods in Engineering , pp. 55-70
    • Wendland, W.L.1
  • 60
    • 0000096635 scopus 로고
    • Strongly elliptic boundary integral equations
    • Iserles A., Powell M., (eds), Oxford: Clarendon Press,. Edited by
    • Wendland, W.L., 1987. “ Strongly elliptic boundary integral equations ”. In The State of the Art in Numerical Analysis, Edited by: Iserles, A., and Powell, M., 511–561. Oxford: Clarendon Press.
    • (1987) The State of the Art in Numerical Analysis , pp. 511-561
    • Wendland, W.L.1
  • 61
    • 0001506755 scopus 로고
    • On asymptotic error estimates for the combined BEM and FEM. In CISM Lecture Notes 301
    • Stein E., Wendland W.L., (eds), Udine: Springer-Verlag, Wien-New York,. Edited by
    • Wendland, W.L., 1988. “ On asymptotic error estimates for the combined BEM and FEM. In CISM Lecture Notes 301 ”. In Finite Element and Boundary Element Techniques from Mathematical and Engineering point of view, Edited by: Stein, E., and Wendland, W.L., 273–333. Udine: Springer-Verlag. Wien-New York
    • (1988) Finite Element and Boundary Element Techniques from Mathematical and Engineering point of view , pp. 273-333
    • Wendland, W.L.1
  • 63
    • 0006096210 scopus 로고
    • Marriage á la mode - The best of both worlds (finite elements and boundary integrals)
    • Glowinski R., (ed), Chichester: John Wiley and Sons, Newyork, Brisbane and Toronto, and,. Edited by
    • Zienkiewicz, O.C., Kelly, D.W., and Bettess, P., 1979. “ Marriage á la mode - The best of both worlds (finite elements and boundary integrals) ”. In In Energy Methods in Finite Element Analysis, chapter 5, Edited by: Glowinski, R., 81–107. Chichester: John Wiley and Sons. Newyork, Brisbane and Toronto
    • (1979) In Energy Methods in Finite Element Analysis, chapter 5 , pp. 81-107
    • Zienkiewicz, O.C.1    Kelly, D.W.2    Bettess, P.3


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