Finite element analysis of sloshing and hydroelastic vibrations under gravity
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 305-327. 
@article{M2AN_1999__33_2_305_0,
     author = {Berm\'udez, Alfredo and Rodr{\'\i}guez, Rodolfo},
     title = {Finite element analysis of sloshing and hydroelastic vibrations under gravity},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {305--327},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {2},
     year = {1999},
     mrnumber = {1700037},
     zbl = {0961.74057},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_2_305_0/}
}
TY  - JOUR
AU  - Bermúdez, Alfredo
AU  - Rodríguez, Rodolfo
TI  - Finite element analysis of sloshing and hydroelastic vibrations under gravity
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 305
EP  - 327
VL  - 33
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_2_305_0/
LA  - en
ID  - M2AN_1999__33_2_305_0
ER  - 
%0 Journal Article
%A Bermúdez, Alfredo
%A Rodríguez, Rodolfo
%T Finite element analysis of sloshing and hydroelastic vibrations under gravity
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 305-327
%V 33
%N 2
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_1999__33_2_305_0/
%G en
%F M2AN_1999__33_2_305_0
Bermúdez, Alfredo; Rodríguez, Rodolfo. Finite element analysis of sloshing and hydroelastic vibrations under gravity. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 305-327. http://www.numdam.org/item/M2AN_1999__33_2_305_0/

[1] I. Babusška and J. Osborn, Eigenvalue problems, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions Eds., North Holland, Amsterdam (1991). | MR | Zbl

[2] H. Berger, J. Boujot and R. Ohayon, On a spectral problem in vibration mechanics: computation of elastic tanks partially filled with liquids. J. Math. Anal. Appl. 51 (1975) 272-298. | MR | Zbl

[3] A. Bermúdez, R. Durán, M.A. Muschietti, R. Rodriguez and J. Solomin, Finite element vibration analysis of fluid-solid Systemswithout spurious modes. SIAM J. Numer. Anal 32 (1995) 1280-1295. | MR | Zbl

[4] A. Bermúdez, R. Durán and R. Rodriguez, Finite element analysis of compressible and incompressible fluid-solid Systems. Math. Comp. 67 (1998) 111-136. | MR | Zbl

[5] A. Bermúdez and R. Rodríguez, Finite element computation of the vibration modes of a fluid-solid system. Comp. Methods Appl. Mech. Eng. 119 (1994) 355-370. | MR | Zbl

[6] J. Boujot, Sur l'analyse des caractéristiques vibratoirs d'un liquide contenu dans un reservoir. J. Mécanique 11 (1972) 647-671. | MR | Zbl

[7] J. Boujot, Mathematical formulation of fluid-structure interaction problems. RAIRO Modél. Math. Anal. Numér. 21 (1987) 239-260. | Numdam | MR | Zbl

[8] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). | MR | Zbl

[9] P. Clement, Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | MR | Zbl

[10] C. Conca, J. Planchard and M. Vanninathan, Fluids and Periodic Structures. Masson, Paris (1992). | Zbl

[11] J. Descloux, N. Nassif and J. Rappaz, On spectral approximation. Part I: The problem of convergence. Part 2: Error estimates for the Galerkin methods. RAIRO Anal. Numér. 12 (1978) 97-119. | Numdam | MR | Zbl

[12] V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1986). | MR | Zbl

[13] P. Grisvard, Elliptic Problems for Non-smooth Domains. Pitman, Boston (1985). | Zbl

[14] T. Kato, Perturbation Theory for Linear Operators. Springer Verlag, Berlin (1966). | MR | Zbl

[15] M. Hamdi, Y. Ouset and G. Verchery, A displacement method for the analysis of vibrations of coupled fluid-structure Systems, Internat. J. Numer. Methods Eng. 13 (1978) 139-150. | Zbl

[16] J. Mandel, Cours de Mécanique des Milieux Continus. Gauthier-Villars, Paris (1966). | Zbl

[17] H.J-P. Morand and R. Ohayon, Interactions Fluides-Structures, Recherches en Mathématiques Appliquées. Masson, Paris 23 (1992). | MR | Zbl

[18] R. Rodríguez and J. Solomin, The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. Math. Comp. 65 (1996) 1463-1475. | MR | Zbl

[19] R.M.S.M. Schulkes, Interactions of an elastic solid with a viscous fluid: eigenmode analysis. J. Comput. Phys.100 (1992) 270-283. | MR | Zbl

[20] P.A. Raviart and J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of Finite Element Methods, Lecture Notes in Mathematics. Springer Verlag, Berlin, Heidelberg, New York 606 (1977) 292-315. | MR | Zbl

[21] P. Tong, Liquid sloshing in an elastic container. AFOSR 66-0943, California Institute of Technology, Pasadena, CA (1966).