Finite element analysis of sloshing and hydroelastic vibrations under gravity
Alfredo Bermúdez, Rodolfo Rodríguez (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Alfredo Bermúdez, Rodolfo Rodríguez (1999)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
Mauricio A. Barrientos, Gabriel N. Gatica, Rodolfo Rodríguez, Marcela E. Torrejón (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....
Marco Picasso, Jacques Rappaz (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are...
Christine Bernardi, Frédéric Hecht, Olivier Pironneau (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization...
Andrea Bonito, Philippe Clément, Marco Picasso (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
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A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded. A finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, so as error estimates, using an implicit function theorem and regularity results obtained in [Bonito (2006) 381–398] for the solution of the continuous problem. error estimates are also derived. Numerical results with...