Accueil du LMA

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Méthodes Numériques pour les Fluides

Jeudi 04 Décembre 2008
Ecole Nationale des Ponts et Chaussées
Salle B414 - Aile Belgrand - 4 eme étage
77420 Champs sur Marne

(Pas d'inscription - participation libre)

Acces: RER A, station Noisy-Champs, sortie 3, cite Descartes
              (25 minutes depuis Paris)

10h15-10h45 : Accueil / Café

10h45-11h45 :  ShiPeng Mao (Inst. Comp. Math, Beijing)
Anisotropic finite elements with their applications » 

The classical convergence analysis of FEM is based on the non-degenerate conditions 
of meshes, which is a rstriction both in the theory and applications of FEM, therefore, the 
theme of this talk is the convergence analysis of FEM methods on anisotropic meshes


11h45-12h45 : Claire Chainais-Hillairet (Univ. Clermont-Ferrand)
« Finite volume schemes for non-coercive elliptic problems»

      We present the numerical analysis of some general finite volume
        schemes for convection-diffusion equations with Neumann boundary
        conditions. In this case, the continuous problem has a kernel. We prove
        that the schemes satisfy the same properties as the continuous problem
        and that the kernel of the scheme and the approximate solution respectively
        converge to the kernel and the solution of the problem. Finally, we show
        numerical experiments in order to compare some particular schemes
        (centered, upwind and Scharfetter-Gummel schemes) included in the
        general framework.
        It is a joint work with J. Droniou.


12h00-14h30 : Pause Repas

14h30-15h15 : Christophe Le Potier (CEA- SFME/MTMS)
« A linear scheme on irregular grids for anisotropic diffusion problems
satisfying the maximum principle

We introduce a finite-difference method for anisotropic diffusion
operators on distorted grids. We calculate the second-order derivatives
in space using a Taylor expansion. Thanks to a certain assumption on the
grid properties, we show the convergence of the scheme and a discrete
maximum principle.
The efficiency of the algorithm is demonstrated by comparing it with
analytical solutions and with results obtained by other numerical schemes.



15h15-16h00 : Leo Agelas (Inst. Francais du Petrole )
« Centered finite volume schemes for diffusion problems on general grids in
anisotropic media

We address finite volume schemes for anisotropic/heterogeneous problems.
We prove a convergence result on general grids, assuming a piecewise regular 
diffusion tensor, the consistency of the numerical flux and the coercivity of the 
discrete bilinear form. Numerical results will be displayed 
for several finite volumes schemes.


16h00-16h15 : Café

16h15-17h00 : Daniela Capatina & David Trujillo (Univ. Pau)
« Stabilized finite element method for Navier-Stokes equations
with physical boundary conditions

This talk deals with the numerical approximation of the 2D and 3D Navier-Stokes 
equations, satisfying nonstandard boundary conditions. This lays on the F.E. discretisation 
of the corresponding Stokes problem, which is achieved through a three-fields stabilized 
mixed formulation. A priori and a posteriori error bounds are established for the nonlinear 
problem, ascertaining the convergence of the method. Finally, numerical tests are 
presented, including mesh refinement via error indicators.


Organisation :

            Secrétariat : M. Ouhanna (ENPC/Champs sur Marne)

Acces: RER A, station Noisy-Champs, sortie 3, cite Descartes
              (25 minutes depuis Paris)