On the coupling of boundary integral and finite element methods with nonlinear transmission conditions

Applicable Analysis

Volumn 62, Issue 1-2, 1996, Pages 181-210

  Barrenechea, Gabriel R ^a   Gatica, Gabriel N ^a  

^a NONE

Author keywords

Boundary integral method; Coupling procedure; Finite elements; Nonlinear flux

Indexed keywords

EID: 85013976756     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819608840477     Document Type: Article

References (45)

1. Barrenechea G. R., Coupling of Boundary Elements and Finite Elements for Znlerface Problems with Nonlznear Transmission Condrtzons (in spanish), Thesis of Mathematical Engineer Universidad de Concepción 1996
2. Barrenechea G. R., Gatica G. N., Numerical analysis of the coupled BIM and FEM with nonlinear transmission conditions 1996 In preparation
3. Berger, H., 1989. Convergent finite element formulations for transonic flows. Numerische, 56 (5): 425–447.
4. Berger, H., warnecke, G., and Wendland, W. L., 1990. Finite elements for transonic potential flows. Numerical Methods for Partial Differential Equations, 6 (1): 17–42.
5. Brezzi, F., 1979. On the coupling of boundary integral and finite element methods. Calcolo, 16: 189–201.
6. Brink U., Carstensen C., Stein E., Symmetric coupling of boundary elements and Kaviart-Thomas type mixed finite elements in elastostatics 1994 SIAM Journal on Numerical.lnalyszs, to appear
7. Ciarlet, P., 1978. “The Finite Element Method for Elltptic Problems ”. In s, North Holland: Amsterdam.
8. Costabel, M., 1987. “ Symmetric methods for the coupling of finite elements and boundary elements ”. In In Boundary Elements IX, vol., Edited by: Brebbia, C.A., 411–420. Berlin: Springer-Verlag.
9. Costabel, M., 1988. Boundary integral operators on Lipschitz domains: Elementary results. SIAM Journal on Mathematzcal Analysis, 19: 613–626.
10. Costabel, H., 1989. “ on the coupling of finite and boundary element methods ”. In In Procedding of the Internatical Symposium on Numetical Analysis., Edited by: Karasózen, B., 1–14. Mute: Ankara.
11. 3 ”. In In Mathematics of Finite Elements and.Applications, Edited by: Whiteman, J.R., Vol. VI, 289–296. London: Academic Press.
12. Costabel, M., 1988. “ Coupling of finite elements and boundary elements for transmission problems of elastic waves ”. In In IUTAM Symposrzdm on Advanced, Edited by: Cruse, T.A., 117–124. New York&Berlin: Springer-Verlag.
13. Costabel, M., and Stephan, E.P., 1990. Coupling of finite and boundary element methods for an elasto-plast, ic interface problem. SIAM Journal on Numerical Analysis, 27 (5): 1212–1226.
14. Feistauer, M., 1986. Mathematical and numerical study of nonlinear problems in fluid mechanics. Iii, Edited by: Vosniansky, J., and Zlamal, M., 3–16. New York, Berlin Heidelberg: Springer. eds., Proc. Conf. Equadiff 6, Brno 1985
15. Feistauer, M., and Zenisek, A., 1987. Finite element sohtion of nonlinear elliptic problems. Numerzsche Mathematik, 50: 451–475.
16. Gatica, G. N., 19789. On the Coupling of Boundary Integral and Finlte Element Methods for Nonlznear Boundary Value Problems. Ph.D. Dissertation. 19789. University of Delaware.
17. Gatica, G.N., 1989. The coupling of boundary element and finite elemet methods for a nonlinear exterior boundary value problem. Zeitschrzft fur Analyszs, 8 (4): 377–387.
18. 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.
19. 2 . Numerische Mathematik, 61 (2): 171–214.
20. 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 Optzmization, 13 (5&6): 431–447.
21. Gatica, 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: 442–461.
22. Gatica, G.N., and Hsiao, G.C., 1995b. “ Boundary-Field Equation Methods for a Class of Nonlinear Problems ”. Vol. 331, Pitman Research Notes in Mathematics Series.
23. Gatica, G. N., and Wendland, W. L., Coupling of mixed finite elements and boundary elements for linear and nonlinear elliptic problems. Technical Report 94-08. 1972/73. Departamento de Ingenieria Matemiitica, Universidad de Concepcion.
24. Gatica, G. N., and Wendland, W. L., Coupling of mixed finite elements and boundary elements for an hyperelastic interface problem. Technical Report 95-04. 1972/73. Departamento de Ingenieria Matematica, Universidad de Concepción.
25. 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.
26. Han, H., 1990. A new class of variational formulations for the coupling of finite and boundary element methods. Journal of Computational Mathematics, 8 (3): 223–232.
27. Hsiao, G.C., 1990. The coupling of boundary element and finite element methods. A plenary lecture at t, he GAMM-Tagung 1989. Zeitschrift fur Angewandte Mathematik und Mechanics (ZAMM), 70 (6): 493–503.
28. Hsiao G.C., Some recent developments on the coupling of finite element and boundary element methods. Rend. Sem. Mat. Univers. Politecn. Torino 1996 Fascicolo Speciale, Numerical Methods.
29. 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.
30. Johnson, C., and Nedelec, J. C., 1980. On the coupling of boundary integral and finite. Mathematics of Computation, 35: 1063–1079.
31. Langer, U., 1994. “ arallel iterative solution of symmetric coupled FE/BE-equations via domain decomposition ”. In In Contemporary Mathematics, Edited by: Quarteroni, A., Vol. 157, Providence, Rhode Island.: American Mathematical Society. Domain Decomposition Methods in Science and Engineering
32. Leroux, M. N., 1977. Methode d'elements finis pour le resolution numerique de problkmes extkrieurs en dimension 2. RAIRO Anal. Numer, 11: 27–60.
33. MacCamy, R. C., and Marin, S. P., 1980. A finite element method for exterior interface problems. Internatzonal Journal of Mathematics and Mathematical Sczences, 3: 311–350.
34. Necas, J., 1986. “ Introductzon to the Theory of Nonlinear Elliptic Equatzons ”. John Wiley and Sons.
35. Polizzotto, C., 1998. “ A consistent formulation of the BEM within elasto-plasticity ”. In In Advanced Boundary Elements Methods, Edited by: Cruse, T.A., Berlin: Springer-Verlag.
36. Polizzotto, C., and Zito, M., 1994. Variational formulations for coupled BE/FE methods in elastostatics. Zeitschrrft fur Angewandte Mathematgk und Mechanics (ZAMM), 74 (11): 533–543.
37. Rohsenov, W.M, and Hartnett, J. P., 1971. “ Handbook of Heat Transfer ”. Book Company: MacGraw-Hill.
38. Ruotsalainen, K., and Wendland, W.L., 1988. On the boundary element methods for. Numerische Mathematik, 53: 299–314.
39. Sequeira, A., 1983. The coupling of boundary integral and finite element methods for the bidimensional exterior steady Stokes problem. Mathematical Methods zn the Applied Sciences, 5: 356–375.
40. Sequeira, A., 1986. On the computer implementation of a coupled boundary and finite element method for the bidimensional exterior steady Stokes problem. Mathematical, 8: 117–133.
41. 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.
42. Vainberg, M.I., 1964. “ OVariational Methods for the Study of Nonlinear Operators ”. In Ph.D. Thesis, Holden-Day, San Francisco, London: Amsterdam.
43. Wendland, W. L., 1986. “ On asymptotic error estimates for the combined BEM and FEM. ”. In In Innovative Numerical Methods zn Engineering, Edited by: Shaw, R.P., 55–70. Springer-Verlag.
44. Wendland, W.L., 1988. “ On asymptotic error estimates for the combined BEM and FEM. ”. In Finite Element and Boundary Element Techniques from, Edited by: Stein, E., and Wendland, W.L., 273–333. Wien-New York, Udine: Springer-Verlag.
45. Zenisek, A., 1981. Discrete forms of Friedrich's inequalities in the finite element. RAIRO Anal. Numer, 15: 265–286.