Weak solutions of fluid-solid interaction problems

Mathematische Nachrichten

Volumn 218, Issue , 2000, Pages 139-163

  Hsiao, George C ^a   Kleinman, Ralph E ^a   Roach, Gary F ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Boundary integral equations; Elasticity; Fluid solid interaction; Fundamental solution; Garding's inquality; Sesquilinear form; Sobolev space; Variational formulation; Weak solution

Indexed keywords

EID: 0038396651     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200010)218:1<139::aid-mana139>3.0.co;2-s     Document Type: Article

References (29)

1. ADAMS, R. A.: Sobolev Spaces, Academic Press, New York, 1975
2. AHNER, J. F., and HSIAO, G. C.: A Neumann Series Representation for Solutions to Boundary Value Problems in Dynamic Elasticity, Quart. J. Appl. Math. (1975), 78-80
3. BATCHELOR, G. K.: An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967
4. BIELAK, J., and MACCAMY, R. C.: Symmetric Finite Element and Boundary Integral Coupling Methods for Fluid-Solid Interaction, I, Quart. J. Appl. Math. 49 (1991), 107-119
5. BURTON, A. J., and MILLER, G. F.: The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems, Proc. Roy. Soc. London, Ser. A, 323 (1971), 201-210
6. COSTABEL, M.: Boundary Integral Operators on Lipschitz Domains: Elementary Results, SIAM J. Math. Anal. 19 (1988), 613-626
7. COSTABEL, M., and STEPHAN, E. P.: Coupling of Finite Elements and Boundary Elements for Transmission Problems of Elastic Waves. In: Symposium on Advanced Boundary Elements, J. CRUSE, et al, Eds., 1987
8. COSTABEL, M., and WENDLAND, L. W.: Strongly Ellipticity of Boundary Integral Operators, J. Reine angew. Mathematik 372 (1986), 34-63
9. DAUTRY, R., and LIONS, J. L.: Mathematical Analysis and Numerical Methods for Science and Technology Vol. 4, Springer-Verlag, Berlin, 1990
10. FRIEDMAN, A.: Partial Differential Equations, Holt, Rinehart, Winston, New York, 1969
11. HAMDI, M. A., and JEAN, P.: A Mixed Functional for Numerical Resolution of Fluid-Structure Interaction Problems. In: Aero- and Hydro-Acoustics IUTAM Symposium, G. COMTEBELLOT and J. E. WILLIAMS, Edr., pp. 269-276, Springer-Verlag, Heidelberg, 1985
12. HAN, H.: A New Class of Variational Formulations for the Coupling of Finite and Boundary Element Methods, Tsinghua University preprint, 1987
13. HSIAO, G. C.: The Coupling of BEM and FEM - a Breif Review. In: Boundary Elements X, C. A. BREBBIA, Ed., pp. 431-441, Springer-Verlag, New York, 1988
14. HSIAO, G. C.: The Coupling of Boundary Element and Finite Element Methods, Z. angew. Math. Mech. (ZAMM) 70, 6 (1990), T493-T503
15. HSIAO, G. C.: On the Boundary-Filed Equation Methods for Fluid-Structure Interactions. In: Problems and Methods in Mathematical Physics, L. JENTSCH and F. Tröltzsch, Eds., Teubner-Text zur Mathematik, Band 34 (1994), 79-88, B.G. Teubner Veriagsgesellschaft, Stuttgart
16. HSIAO, G. C., KLEINMAN, R. E., and SCHUETZ, C. S.: On Variational Formulations of Boundary Value Problems for Fluid-Solid Interactions. In: Elastic Wave Propagation, M. F. MCCARTHY and M. A. HAYES, Ed., pp. 321-326, North-Holland, Amsterdam, 1989
17. HSIAO, G. C., and WENDLAND, W. L.: A Finite Element Method for an Integral Equation of the First Kind, J. Math. Anal. Appl. 58 (1977), 449-481
18. HSIAO, G. C., and WENDLAND, W. L.: The Aubin-Nitsche Lemma for Integral Equations, J. of Integral Equation 3 (1981), 299-315
19. HSIAO, G. C., and WENDLAND, W. L.: On a Boundary Integral Method for Some Exterior Problems in Elasticity, Proceeding of Tbilisi University, pp. 31-60, Tbilisi University Press, Tbilisi, 1985
20. JOHNSON, C., and NEDELEC, J. C.: On the Coupling of Boundary Integral and Finite Element Methods, Math. Comp. 35 (1980), 1063-1079
21. JONES, D.S.: Integral Equations for the Exterior Acoustic Problems, Quart. J. of Mech. Appl. Math. 22 (1974), 129-142
22. JONES, D.S.: Low-Frequency Scattering by a Body in Lubricated Contact, Quart. J. Mech. Appl. Math. 36 (1983), 111-137
23. JONES, D. S.: A Uniqueness Theorem in Elastodynamics, Quart. J. Mech. Appl. Math. 37 (1984), 121-142
24. KLEINMAN, R. E., and ROACH, G. F.: On Modified Green's Functions in the Exterior Problems for the Helmholtz Equation, Proc. Roy. Soc. London, Ser. A, 383 (1982), 313-332
25. KUPRADZE, V. D.: Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, 1965
26. LUKE, C. J., and MARTIN, P.A.: Fulid-Solid Interaction: Acoustic Scattering by a Smooth Elastic Obstacle, SIAM J. Appl. Math. 55 (1995), 904-922
27. MAZ'YA, V. G.: Boundary Integral Equations, in Analysis IV, Encyclopaedia of Mathematical Sciences Vol. 27, Springer-Verlag, Berlin, Heidelberg, 1991
28. PAO, Y. H., and VARATHARAJULU, V.: Huygen's Principle, Radiation Conditions, and Integral Formulas for the Scattering of Elastic Waves, J. Acoust. Soc. of Amer. 59 (1976), 1361-1371
29. URSELL, F.: On the Exterior Problems of Acoustics: II, Math. Proc. Camb. Phil. Soc. 84 (1978), 545-548