An overlapping additive Schwarz-Richardson method for monotone nonlinear parabolic problems.
An unconditionally stable finite element scheme for anisotropic curve shortening flow
Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method.
An unconditionally stable pressure correction scheme for the compressible barotropic Navier-Stokes equations
We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution. The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...
An upper bound for positive solutions of the equation .
An upper bound for the local time-decay of scattering solutions for the Schrödinger equation with Coulomb potential
An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition
We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness...
An upwind finite element method for singularly perturbed elliptic problems and local estimates in the -norm
Análisis de las singularidades de una ecuación diferencial fraccionaria no lineal.
Se exponen las estimaciones numéricas preliminares de las singularidades de una ecuación diferencial fraccionaria no lineal. Dicha ecuación aparece en el estudio de las ondas viajeras asociadas a una ecuación de ondas que es una interpolación entre la ecuación de ondas clásica y la ecuación de Benjamin-Ono.
Analogue d'un Lemme de Kohn et Nirenberg
Analycity of the Semigroup Generated by the Stokes Operator.
Analyse 2-microlocale et équations d'Euler incompressible
Analyse de sensibilité d’un problème de contrôle optimal bilinéaire
Dans cet article, nous étudions la sensibilité d’un problème de contrôle optimal de type bilinéaire. Le coût est différentiable, quadratique et strictement convexe. Le système est gouverné par un opérateur parabolique du quatrième ordre et présente une perturbation additive dans l’équation d’état, ainsi qu’une partie bilinéaire, relativement au contrôle et à l’état , de la forme . Sous des conditions de petitesse de l’état initial et de la perturbation, nous exploitons les propriétés de régularité...
Analyse d'un élément mixte pour le problème de Stokes . I. Résultats générauax.
Analyse d'un élément mixte pour le problème de Stokes . II. Construction et estimations d'erreur.
Analyse d'une formulation à trois champs du problème de Stokes
Analyse harmonique non linéaire
Analyse limite d'équations variationnelles dans un domaine contenant une grille
Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.
The aim of the paper is an analytical and numerical approach to the pseudo-compositional black-oil model for simulating a 3-D isothermal constrained polyphasic flow in porous media, taking into account realistic boundary conditions. The handling of the component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and first-order hyperbolic inequalities: the introduction of unilateral problems arises from the nature of the thermodynamical equilibrium...
Analyse mathématique des transferts thermiques dans des systèmes dispersés subissant des transformations de phases
Analyse microlocale et équations d’évolution