Crouseilles, Nicolas Mehrenberger, Michel Vecil, Francesco

In this paper, we test an innovative numerical scheme for the simulation of the guiding-center model, of interest in the domain of plasma physics, namely for fusion devices. We propose a 1D Discontinuous Galerkin (DG) discretization, whose basis are the Lagrange polynomials interpolating the Gauss points inside each cell, coupled to a conservative ...

Angot, Philippe Keating, Johnwill Minev, Peter D. Minev, Peter

The paper proposes and examines the stability and convergence properties of an extension of the direction splitting methods towards parabolic and incompressible flow problems in complex, possibly time dependent geometries. Two possible spatial discretization are considered. One of them is based on a fictitious domain procedure and the other one is ...

Delourme, Bérangère Claeys, Xavier

This work deals with the scattering of acoustic waves by a thin ring that contains many regularly-spaced heterogeneities. We provide and justify a complete description of the solution with respect to the period and the thickness of the heterogeneities. Our approach mixes matched asymptotic expansions and homogenization theory.

Araya, Ignacio Neveu, Bertrand Trombettoni, Gilles

In interval arithmetics, special care has been brought to the definition of interval extension functions that compute narrow interval images. In particular, when a function f is monotonic w.r.t. a variable in a given domain, it is well-known that the monotonicity-based interval extension of f computes a sharper (interval) image than the natural int...

Abgrall, Remi Congedo, Pietro Marco

This paper deals with the formulation of a semi-intrusive (SI) method allowing the computation of statistics of linear and non linear PDEs solutions. This method shows to be very efficient to deal with probability density function of whatsoever form, long-term integration and discontinuities in stochastic space. Given a stochastic PDE where randomn...

Moya, Ludovic

An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size restrictions c...

Bécache, Eliane Prieto, Andres

This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a general first-order hyperbolic system. Then, in the context of the pressure-velocity formulation of the acoustic...

Herlin, Isabelle Béréziat, Dominique Mercier, Nicolas

Data Assimilation is a well-known mathematical technic used, in environmental sciences, to improve, thanks to observation data, the forecasts obtained by meteorological, oceanographic or air quality simulation models. It aims to solve the evolution equations, describing the dynamics of the state variables, and an observation equation, linking at ea...

Benveniste, Albert Caillaud, Benoît Pouzet, Marc

International audience

Dubach, Eric Luce, Robert Thomas, Jean-Marie

The aim of this paper is to present a new class of mixed finite elements on quadrilaterals and hexahedra where the approximation is polynomial on each element K. The degrees of freedom are the same as those of classical mixed finite elements. However, in general, with this kind of finite elements, the resolution of second order elliptic problems le...