@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] Eigenvalue problems, in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions Eds., North Holland, Amsterdam (1991). | MR | Zbl
and ,[2] 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
, and ,[3] Finite element vibration analysis of fluid-solid Systemswithout spurious modes. SIAM J. Numer. Anal 32 (1995) 1280-1295. | MR | Zbl
, , , and ,[4] Finite element analysis of compressible and incompressible fluid-solid Systems. Math. Comp. 67 (1998) 111-136. | MR | Zbl
, and ,[5] Finite element computation of the vibration modes of a fluid-solid system. Comp. Methods Appl. Mech. Eng. 119 (1994) 355-370. | MR | Zbl
and ,[6] Sur l'analyse des caractéristiques vibratoirs d'un liquide contenu dans un reservoir. J. Mécanique 11 (1972) 647-671. | MR | Zbl
,[7] Mathematical formulation of fluid-structure interaction problems. RAIRO Modél. Math. Anal. Numér. 21 (1987) 239-260. | Numdam | MR | Zbl
,[8] Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York (1991). | MR | Zbl
and ,[9] Approximation by finite element functions using local regularization. RAIRO Anal. Numér. 9 (1975) 77-84. | Numdam | MR | Zbl
,[10] Fluids and Periodic Structures. Masson, Paris (1992). | Zbl
, and ,[11] 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
, and ,[12] Finite Element Methods for Navier-Stokes Equations. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1986). | MR | Zbl
and ,[13] Elliptic Problems for Non-smooth Domains. Pitman, Boston (1985). | Zbl
,[14] Perturbation Theory for Linear Operators. Springer Verlag, Berlin (1966). | MR | Zbl
,[15] A displacement method for the analysis of vibrations of coupled fluid-structure Systems, Internat. J. Numer. Methods Eng. 13 (1978) 139-150. | Zbl
, and ,[16] Cours de Mécanique des Milieux Continus. Gauthier-Villars, Paris (1966). | Zbl
,[17] Interactions Fluides-Structures, Recherches en Mathématiques Appliquées. Masson, Paris 23 (1992). | MR | Zbl
and ,[18] The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems. Math. Comp. 65 (1996) 1463-1475. | MR | Zbl
and ,[19] Interactions of an elastic solid with a viscous fluid: eigenmode analysis. J. Comput. Phys.100 (1992) 270-283. | MR | Zbl
,[20] 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
and ,[21] Liquid sloshing in an elastic container. AFOSR 66-0943, California Institute of Technology, Pasadena, CA (1966).
,