Displaying similar documents to “Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models”

A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case

Jacques Baranger, Ahmed Machmoum (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the numerical approximation of a first order stationary hyperbolic equation by the method of characteristics with pseudo time step using discontinuous finite elements on a mesh 𝒯 h . For this method, we exhibit a “natural” norm || || for which we show that the discrete variational problem P h k is well posed and we obtain an error estimate. We show that when goes to zero problem ( P h k ) (resp. the || || norm) has as a limit problem ( ) (resp. the || || norm) associated...

On the distribution of free path lengths for the periodic Lorentz gas II

François Golse, Bernt Wennberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Consider the domain Z ϵ = { x ∈ ℝ n ; d i s t ( x , ϵ ℤ n ) > ϵ γ } and let the free path length be defined as τ ϵ ( x , v ) = inf { t > 0 ; x - t v ∈ Z ϵ } . In the Boltzmann-Grad scaling corresponding to γ = n n - 1 , it is shown that the limiting distribution φ ϵ of τ ϵ is bounded from below by an expression of the form , for some . A numerical study seems to indicate that asymptotically for large , φ ϵ ∼ C / t . This is an extension of a previous work [J. Bourgain , (1998) 491-508]. As a consequence, it is proved that the linear Boltzmann type transport equation is inappropriate...