Displaying similar documents to “A priori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem”

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

Gladys Narbona-Reina, Didier Bresch (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Springer Verlag (2010)] and in the present paper, we provide a self-contained description,...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

Yongxing Shen, Adrian J. Lew (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order  ≥ 1 for the approximation of the displacement field, and of order or  − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in both cases, with error estimates that...

Asymptotic-Preserving scheme for a two-fluid Euler-Lorentz model

Stéphane Brull, Pierre Degond, Fabrice Deluzet, Alexandre Mouton (2011)

ESAIM: Proceedings

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The present work is devoted to the simulation of a strongly magnetized plasma as a mixture of an ion fluid and an electron fluid. For simplicity reasons, we assume that each fluid is isothermal and is modelized by Euler equations coupled with a term representing the Lorentz force, and we assume that both Euler systems are coupled through a quasi-neutrality constraint of the form  =  . The numerical...

Multiscale modelling of sound propagation through the lung parenchyma

Paul Cazeaux, Jan S. Hesthaven (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sound through the lung above 1 kHz is known to be highly frequency-dependent. We pursue the key idea that the viscoelastic parenchyma structure is highly heterogeneous on the small scale and use two-scale homogenization techniques to...

Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry and in vivo stress incorporation

Joris Bols, Joris Degroote, Bram Trachet, Benedict Verhegghe, Patrick Segers, Jan Vierendeels (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to conditions. This entails an internal stress state to be present in the measured geometry of a blood vessel due to the presence of the blood pressure. In order to correct for this stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the...

Interface model coupling via prescribed local flux balance

Annalisa Ambroso, Christophe Chalons, Frédéric Coquel, Thomas Galié (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at = 0. The closure pressure laws differ in the domains < 0 and > 0, and a Dirac source term concentrated at = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property...

T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R, with  = 23. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or...