Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.
Ueber eine neue Methode zur Lösung gewisser Randwertaufgaben
Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale
The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based...
Une norme « naturelle » pour la méthode des caractéristiques en éléments finis discontinus : cas 1-D
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
Uniformly exponentially or polynomially stable approximations for second order evolution equations and some applications
In this paper, we consider the approximation of second order evolution equations. It is well known that the approximated system by finite element or finite difference is not uniformly exponentially or polynomially stable with respect to the discretization parameter, even if the continuous system has this property. Our goal is to damp the spurious high frequency modes by introducing numerical viscosity terms in the approximation scheme. With these viscosity terms, we show the exponential or polynomial...
Uniformly exponentially stable approximations for a class of second order evolution equations
We consider the approximation of a class of exponentially stable infinite dimensional linear systems modelling the damped vibrations of one dimensional vibrating systems or of square plates. It is by now well known that the approximating systems obtained by usual finite element or finite difference are not, in general, uniformly stable with respect to the discretization parameter. Our main result shows that, by adding a suitable numerical viscosity term in the numerical scheme, our approximations are...