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Finite element analysis of sloshing and hydroelastic vibrations under gravity

Alfredo Bermúdez, Rodolfo Rodríguez (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with a finite element method to solve fluid-structure interaction problems. More precisely it concerns the numerical computation of harmonic hydroelastic vibrations under gravity. It is based on a displacement formulation for both the fluid and the solid. Gravity effects are included on the free surface of the fluid as well as on the liquid-solid interface. The pressure of the fluid is used as a variable for the theoretical analysis leading to a well posed mixed linear eigenvalue...

Finite element approximation of a contact vector eigenvalue problem

Hennie de Schepper, Roger Van Keer (2003)

Applications of Mathematics

We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error...

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