Finite Dimensional Approximation of Bifurcation Problems in Presence of Symmetries.
Finite element analysis of sloshing and hydroelastic vibrations under gravity
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
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...
Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem
Finite element approximation of the first eigenvalue of a nonlinear problem for some special domains.
Fourth order eigenvalue approximation by extrapolation on domains with reentrant corners.