On the symmetric boundary element method and the symmetric coupling of boundary elements and finite elements

IMA Journal of Numerical Analysis

Volumn 17, Issue 2, 1997, Pages 201-238

  Carstensen, Carsten ^a,b   Wriggers, Peter ^a  

^a UNIVERSITY OF KIEL   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; MACROS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SAILING VESSELS;

CONSTANT COEFFICIENTS; LINEAR ELASTIC MATERIAL; LINEAR PARTIAL DIFFERENTIAL EQUATIONS; MODEL TRANSMISSION; NUMERICAL TREATMENTS; STANDARD FINITE ELEMENT; SYMMETRIC BOUNDARY ELEMENT METHOD; TWO-DIMENSIONAL PROBLEM;

FINITE ELEMENT METHOD;

EID: 0031511881     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/17.2.201     Document Type: Article

References (35)

1. BIELAK, J., & MACCAMY, R. C. 1983 An exterior interface problem in two-dimensional elastodynamics. Quart. Appl. Math. 41, 143-159.
2. BREZZI, F., & JOHNSON, C. 1979 On the coupling of boundary integral and finite element methods. Calcolo 16, 189-201.
3. CARSTENSEN, C. 1993 Interface problem in holonomic elastoplasticity. Math. Methods Appl. Sci. 16, 819-835.
4. CARSTENSEN, C. 1994 Interface problem in viscoplasticity and plasticity. SIAM J. Math. Anal. 25, 1468-1487.
5. CARSTENSEN, C. 1996 Coupling of FEM and BEM for interface problems in viscoplasticity and plasticity with hardening. SIAM J. Numer. Anal. 33, 171-207.
6. CARSTENSEN, C., FUNKEN, S. A., & STEPHAN, E. P. 1996 On the adaptive coupling of FEM and BEM in 2-d-elasticity. Numer. Math. (At Press)
7. CIARLET, P. G. 1978 The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
8. COSTABEL, M. 1987 Symmetric methods for the coupling of finite elements and boundary elements. Boundary Elements IX, vol. 1 (C. A. Brebia et al. eds). Berlin: Springer, pp 411-420.
9. COSTABEL, M. 1988 Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 19, 613-626.
10. COSTABEL, M., & STEPHAN, E. P. 1990a Integral equations for transmission problems in linear elasticity. J. Integr. Eq. Appl. 2, 211-223.
11. COSTABEL, M., & STEPHAN, E. P. 1990b Coupling of finite and boundary element methods for an elastoplastic interface problem. SIAM J. Numer. Anal. 27, 1212-1226.
12. EKELAND, I., & TEMAM, R. 1976 Convex Analysis and Variational Problems. Amsterdam: North-Holland.
13. GATICA, G. N., & HSIAO, G. C. 1989 The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem. Z. Anal. Angew. 8, 377-387.
14. 2. Numer. Math. 61, 171-214.
15. GWINNER, J., & STEPHAN, E. P. 1993 A boundary element procedure for contact problems in plane linear elastostatics. Math. Modelling Numer. Anal. 27, 457-480.
16. HAN, H. 1990 A new class of variational formulations for the coupling of finite and boundary element methods. J. Comput. Math. 8, 223-232.
17. HOLZER, S. 1992 Das symmetrische Randelementverfahren: Numerische Realisierung und Kopplung mit der Finite-Elemente-Methode zur elastoplastischen Strukturanalyse. PhD Thesis, Berichte aus dem konstruktiven Ingenieurbau, 5792, TU Munich.
18. HSIAO, G. C., KOPP, P., & WENDLAND, W. L. 1984 Some applications of a Galerkin-collocation method for boundary integral equations of the first kind. Math. Methods Appl. Sci. 6, 280-325.
19. HSIAO, G. C., STEPHAN, E. P., & WENDLAND, W. L. 1991 On the Dirichlet problem in elasticity for a domain exterior to an arc. J. Comput. Appl. Math. 34, 1-19.
20. HSIAO, G. C., & WENDLAND, W. L. 1985 On a boundary integral method for some exterior problems in elasticity. Proc. Tbilisi Univ. 257, 31-60.
21. JOHNSON, C. 1976a On finite element methods for plasticity problems. Numer. Math. 26, 79-84.
22. JOHNSON, C. 1976b Existence theorems for plasticity problems. J. Math. Pures Appl. 55, 431-444.
23. JOHNSON, C. 1978 On plasticity with hardening. J. Math. Anal. Appl. 62, 325-336.
24. JOHNSON, C., & NEDELEC, J. C. 1980 On the coupling of boundary integral and finite element methods. Math. Comput. 35, 1063-1079.
25. KUPRADZE, V. D., et al 1979 Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. Amsterdam: North-Holland.
26. NEČAS, J., & HLAVÁČEK, I. 1981 Mathematical Theory of Elastic and Elasto-Plastic Bodies. Amsterdam: Elsevier.
27. SIMO, J. C. 1991 Nonlinear stability of the time-discrete variational problem of evolution in nonlinear heat conduction, plasticity and viscoplasticity. Comput. Methods Appl. Mech. Eng. 88, 111-131.
28. SUQUET, P.-M. 1988 Discontinuities and Plasticity in Nonsmooth Mechanics and Applications (CISM Courses 302) (J. J. Moreau and P. D. Panagiotopoulos, eds). New York: Springer, pp 279-341.
29. TEMAM, R. 1985 Mathematical Problems in Plasticity. Paris: Gauthier-Villars.
30. WENDLAND, W. L. 1983 Boundary element methods and their asymptotic convergence. Theoretical Acoustics and Numerical Techniques (CISM Courses 277) (P. Filippi, ed). New York: Springer, pp 135-216.
31. WENDLAND, W. L. 1988 On asymptotic error estimates for combined BEM and FEM. Finite and Boundary Element Techniques From a Mathematical and Engineering Point of View (CISM Courses 301) (E. Stein and W. L. Wendland, eds). New York: Springer, pp 273-331.
32. WENDLAND, W. L., & STEPHAN, E. P. 1990 A hypersingular boundary integral method for two-dimensional screen and crack problems. Arch. Rational Mech. Anal. 112, 363-390.
33. ZEIDLER, E. 1988 Nonlinear Functional Analysis and its Applications IV. New York: Springer.
34. ZIENKIEWICZ, O. C., KELLY, D. W., & BETTESS, P. 1977 'Mariage a la mode'. Proc. Conf. on Innovative Numerical Analysis in Engineering Science CETIM (Paris, 1977).
35. ZIENKIEWICZ, O. C., & TAYLOR, L. 1990 The Finite Element Method. London: McGraw-Hill.