Clémentine Courtès

Clémentine Courtès
University of Strasbourg | UNISTRA · Institut de Recherche Mathématique Avancée

PhD in Mathematics

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14
Publications
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44
Citations

Publications

Publications (14)
Preprint
In this article, we investigate a simple model of notched ferromagnetic nanowires using tools from calculus of variations and critical point theory. Specifically, we focus on the case of a single unimodal notch and establish the existence and uniqueness of the critical point of the energy. This is achieved through a lifting argument, which reduces...
Article
Full-text available
Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are able to take into account heterogeneity features, such as super‐spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are ex...
Preprint
In this paper, we consider a ferromagnetic material of ellipsoidal shape. The associated magnetic moment then has two asymptotically stable opposite equilibria, of the form $\pm\overline{m}$. In order to use these materials for memory storage purposes, it is necessary to know how to control the magnetic moment. We use as a control variable a spatia...
Preprint
Modelling epidemics via classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome, as they are able to take heterogeneity features into account, such as super-spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expe...
Article
This article deals with the numerical analysis of the Cauchy problem for the Korteweg–de Vries equation with a finite difference scheme. We consider the explicit Rusanov scheme for the hyperbolic flux term and a 4-point $\theta $-scheme for the dispersive term. We prove the convergence under a hyperbolic Courant–Friedrichs–Lewy condition when $\the...
Conference Paper
We compute the rate of convergence of forward, backward, and central finite difference \(\theta \)-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initial data.
Article
In this article, we deal with the numerical analysis of finite volume schemes for the Cauchy problem of the abcd-systems. In particular we prove the stability and the first (or second) order of convergence for a broad range of parameters a, b, c and d of the systems.
Preprint
In this article, we propose finite volume schemes for the $abcd$-systems and we establish stability and error estimates. The order of accuracy depends on the so-called BBM-type dispersion coefficients $b$ and $d$. If $bd>0$, the numerical schemes are $O(\Delta t+(\Delta x)^2)$ accurate, while if $bd=0$, we obtain an $O(\Delta t+\Delta x)$ -order of...
Preprint
This article deals with the numerical analysis of the Cauchy problem for the Korteweg-de Vries equation with a finite difference scheme. We consider the Rusanov scheme for the hyperbolic flux term and a 4-points $\theta$-scheme for the dispersive term. We prove the convergence under a hyperbolic Courant-Friedrichs-Lewy condition when $\theta\geq \f...
Thesis
Full-text available
Le but de cette thèse est d’étudier certaines équations aux dérivées partielles hyperboliques-dispersives. Une part importante est consacrée à l’analyse numérique et plus particulièrement à la convergence de schémas aux différences finies pour l’équation de Korteweg-de Vries et les systèmes abcd de Boussinesq. L’étude numérique suit les étapes clas...
Article
Full-text available
In this article, we detail the construction of a physics-based preconditioner. The Schur decomposition is the key point of the method which is tested on two hyperbolic systems : acoustic wave equations and shallow water equations without source term. Some conserved properties between preconditioner and initial operator are discussed, especially the...
Technical Report
Full-text available
Ce rapport est le fruit d’un travail effectué lors de la SEME (Semaine d’Étude Maths En- treprise). Le projet présenté ici a été proposé par Airbus et provient du domaine de l’imagerie radar. Les coûts de calcul de reconstruction d’un signal grâce à ses modes de Fourier sont importants et soumis au théorème de Nyquist-Shannon qui donne les conditio...

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