Chambolle, Antonin Pock, Thomas

We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, of a grey-level image in two dimensions). We discuss the properties of finite differences and finite elements based approach and compare their merits, in particular in terms of error estimates and quality of the reconstructio...

Bossy, Mireille Jabir, Jean Francois Martinez, Kerlyns

We consider the problem of the approximation of the solution of a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^\alpha$, with $\alpha>1$. We propose an (semi-explicit) exponential-Euler scheme and study its convergence through its weak approximation error. To this aim, we analyze the $C^{1,4}$ regul...

Audusse, Emmanuel Boittin, Léa Parisot, Martin

The present paper deals with the modeling and numerical approximation of bed load transport under the action of water. A new shallow water type model is derived from the stratified two-fluid Navier-Stokes equations. Its novelty lies in the magnitude of a viscosity term that leads to a momentum equation of elliptic type. The full model, sediment and...

Ehrlacher, Virginie Fuente-Ruiz, Maria Lombardi, Damiano

In the present work, a method is proposed in order to compute a Canonical Polyadic (CP) approximation of a given tensor. It is based on a greedy method and an adaptation of the TT-SVD method. The proposed approach can be straightforwardly extended to compute rank-k updates in a stable way. Some numerical experiments are proposed, in which the propo...

Sghiar, Mohamed

Inspired by the article [3], the introduction of the function $\hat{\circledS}$ whose integer zeros are the prime numbers, will allow me to demonstrate analytically the Goldbach's conjecture [6], the De Polignac's Conjecture [7], the Legendre's conjecture [9], and Landau's conjecture [10] .

Ern, Alexandre Gudi, Thirupathi Smears, Iain Vohralík, Martin

Given an arbitrary function in H(div), we show that the error attained by the global-best approximation by H(div)-conforming piecewise polynomial Raviart-Thomas-Nédélec elements under additional constraints on the divergence and normal flux on the boundary, is, up to a generic constant, equivalent to the sum of independent local-best approximation ...

Sghiar, Mohamed

Inspired by the article [3], the introduction of the function $\hat{\circledS}$ whose integer zeros are the prime numbers, will allow me to demonstrate analytically the Goldbach's conjecture [6], the De Polignac's Conjecture [7], the Legendre's conjecture [9], and Landau's conjecture [10] .

Besse, Christophe Faye, Grégory

We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchang...

Bernard, Olivier LU, Liu-di Salomon, Julien

This paper focuses on mixing strategies and designing shape of the bottom topographies to enhance the growth of the microalgae in raceway ponds. A physical-biological coupled model is used to describe the growth of the algae. A simple model of a mixing device such as a paddle wheel is also considered. The complete process model was then included in...

Aghili, Joubine De Dreuzy, Jean-Raynald Trenty, Laurent Masson, Roland

This paper presents an extension of Discrete Fracture Matrix (DFM) models to com-positional two-phase Darcy flow accounting for phase transitions and Fickian diffusion. The hybrid-dimensional model is based on nonlinear transmission conditions at matrix fracture (mf) interfaces designed to be consistent with the physical processes. They account in ...