Publication Cover
Applicable Analysis
An International Journal
Volume 63, 1996 - Issue 1-2
32
Views
40
CrossRef citations to date
0
Altmetric
Original Articles

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

, , &
Pages 39-75 | Received 01 Apr 1996, Published online: 20 Jan 2011

References

  • Berger H. Warnecke G. Wendland W.L. Analysis of a FEM/BEM coupling method for transonic flow computations 1996 Math. Comp., to appear.
  • 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 .
  • Braess , D. 1992 . Finite Elemente , Berlin : Springer-Verlag .
  • Brezzi , F. 1974 . On the existence, uniqueness and approximation of saddle point problems arising from lagrangian multipliers . RAIRO Anal. Numer. , 8 : 129 – 151 .
  • Brezzi , F. and Fortin , M. 1991 . Mixed and Hybrid Finite Element Methods , New York : Springer-Verlag .
  • Brezzi , F. and Johnson , C. 1979 . On the coupling of boundary integral and finite element methods . Calcolo , 16 : 189 – 201 .
  • Brink U. Carstensen C. Stein E. Symmetric coupling of boundary elements and Raviart-Thomas type mixed finite elements in elastostatics. Talk in the 6th Kolloquium des DFG-Schwerpunkts Randelementmethoden Schmallenberg 1994 held at , September 28 – October 1, Manuscript in preparation..
  • 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 .
  • 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 .
  • 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 .
  • Costabel , M. 1988 . Boundary integral operators on Lipschitz domains: Elementary results . SIAM Journal on Mathematical Analysis , 19 : 613 – 626 .
  • 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 .
  • Costabel , M. and Stephan , E.P. 1988 . “ Coupling of finite elements and boundary elements for inhomogeneous transmission problems in R3 ” . In In Mathematics of Finite Elements and Applications VI , Edited by: Whiteman , J.R. 289 – 296 . London : Academic Press .
  • 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
  • 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 .
  • Duvaut , G. and Lions , J.L. 1971 . Les Inéquations en Mécanique et en Physique , Paris : Dunod .
  • Feng , K. 1983 . “ Finite element method and natural boundary reduction ” . In In Proc. Inter. Congress of Mathematics , 1439 – 1453 . Warsaw : Polish Academy of Sciences .
  • 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 .
  • 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 .
  • Gatica , G.N. and Hsiao , G.C. 1992 . On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in R2 . Numerische Mathematik , 61 ( 2 ) : 171 – 214 .
  • 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 .
  • 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 .
  • 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
  • Girault , V. and Raviart , P.A. 1986 . “ Finite Element Methods for Navier-Stokes Equations ” . In Theory and Algorithms , Berlin : Springer-verlag .
  • 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 .
  • 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 .
  • 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 .
  • Heise , B. 1993 . Nonlinear field calculations with multigrid-Newton methods . Impact of Computing in Science and Engineering , 5 ( 3 ) : 75 – 110 .
  • 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 .
  • Herrmann , L.R. 1967 . Finite element bending analysis for plates . J. Eng. Mech. Div. ASCE , 93 ( 5 ) : 13 – 26 .
  • Hörmander , L. 1963 . Linear Partial Differential Operators , Berlin : Springer-Verlag . Heidelberg, Newyork
  • 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 .
  • 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 .
  • Hsiao G.C. Some recent developments on the coupling of finite element and boundary element methods. Univers. Politecn. Torino 1991 Rend. Sem. Mat., Fascicolo Speciale, Numerical Methods
  • Hsiao G.C. Khoromskij B.N. wendland W.L. Boundary integral operators and domain decomposition, 1996 (U.Stuttgart, MIA Preprint Nr.94-11),submitted.
  • 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 .
  • 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 .
  • 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 .
  • Hsiao , G.C. and Wendland , W.L. 1977 . A finite element method for some integral equations of the first kind . Journal of Mathematical Analysis and Applications , 58 : 449 – 481 .
  • Johnson , C. and Nedelec , J.C. 1980 . On the coupling of boundary integral and finite element methods . Mathematics of Computation , 35 : 1063 – 1079 .
  • Kaitai , L. and Yinnian , H. 1993 . Coupling method for the exterior stationary Navier-Stokes equations . Numerical Methods for Partial Differential Equations , 9 : 35 – 49 .
  • 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 .
  • 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 .
  • Lions , J.L. and Magenes , E. 1972 . Non-Homogeneous Boundary Value Problems and Applications , Berlin : Springer-Verlag . Newyork, Heidelberg
  • Marin , S.P. 1980 . A finite element method for exteior interface problems . International Journal of Mathematics and Mathematical Sciences , 3 : 311 – 350 .
  • Neċcas , J. 1967 . Les Méthodes Directes en Théorie des Equations Elliptiques , Paris : Academia, Prague and Masson .
  • Nċas , J. 1986 . Introduction to the Theory of Nonlinear Elliptic Equations , John Wiley and Sons .
  • 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 .
  • 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 .
  • Polizzotto , C. and Zito , M. 1994 . Variational formulations for coupled BE/FE methods in elastostatics . Zeitschrift fur Angewandte Mathematik und Mechanics (ZAMM) , 74 ( 11 ) : 533 – 543 .
  • 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.
  • 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)
  • Schechter , M. 1971 . Principles of Functional Analysis , Academic Press .
  • 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 .
  • 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 .
  • Sirtori , S. 1979 . General stress analysis by means of integral equations and boundary elements . Meccanica , 14 : 216 – 218 .
  • 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 .
  • Temam , R. 1977 . Navier-Stokes Equations , Amsterdam : North-Holland .
  • 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 .
  • 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 .
  • 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
  • Zienkiewicz , O.C. , Kelly , D.W. and Bettess , P. 1977 . The coupling of the finite element method and boundary solution procedures . International Journal of Numerical Methods in Enginering , 11 : 335 – 375 .
  • 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

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.