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Abdessatar Khlifi
Abdessatar Khlifi
Asymptotic expansion for the Maxwell’s eigenvalue problem in the presence of small deformation
Nous dérivons des formules asymptotiques rigoureuses pour les perturbations des fréquences propres d'un système de Maxwell dues à de petits changements dans l'interface d'une inclusion. Tirant parti des petites perturbations, nous utilisons une analyse asymptotique rigoureuse pour développer une formule asymptotique pour le cas où la valeur propre du problème de référence est simple ou multiple. Nous montrons que nos formules asymptotiques peuvent être exprimées en termes de permittivité électrique et de fonction de profil h modélisant la perturbation de la forme géométrique.
Lahcène Chorfi
Lahcène Chorfi
Khalil Mansouri
Khalil Mansouri
Saber Amdouni
Saber Amdouni
A Priori Error Estimate for the Data Completion Problem in Linear Elasticity
This talk focuses on the finite element analysis of data completion problems in linear elasticity equations. The problem is reformulated as a variational optimal control problem, where the Dirichlet control is defined within the energy space. Building upon prior studies, this work makes a significant contribution by deriving an optimal a priori error estimate. The result demonstrates that, for sufficiently regular data and employing a finite element method of order k, a convergence rate of at least k/3 is achieved. Numerical experiments are provided to support and validate the theoretical results.
Siwar Saidane
Siwar Saidane
Yosra Boukari
Yosra Boukari
Crack identification in a multi layer domain
This talk deals with the identification of cracks in a non-homogeneous multilayer domain with a piece wise constant index of medium. Specifically, it considers the case of scattering by crack with a modified impedance boundary condition.
We propose a method that combines a data completion algorithm with the Reciprocity Gap-Linear Sampling Method (RG-LSM) to detect cracks. The data completion algorithm recovers missing information using Cauchy data from the exterior boundary, extending the RG-LSM’s application in such domains. We validate the robustness of the method through a theoretical analysis and 3D numerical tests, showing its effectiveness on various crack shapes and different noise levels.
Imane Boussetouan
Imane Boussetouan
On Stokes and Navier-Stokes equations with mixed boundary conditions involving the friction
In this work, we consider mixed physical boundary conditions associated to the Stokes and Navier-Stokes systems. Firstly, we study the Stokes equation with Dirichlet boundary condition on some part of the boundary and Navier-type boundary condition on the remaining part. We prove the existence and uniqueness of weak and strong solutions of the corresponding problem in the Hilbert setting. Then, we generalize our solutions to the L p -theory, by means of a duality argument. Secondly, we assume that the non-homogeneous Navier boundary condition is prescribed on one part of the boundary and Dirichlet boundary condition on the other part. We prove the existence and uniqueness of generalized solutions by taking into account the regularity of the friction coefficient, considered as a function. Finally, we extend the obtained results to the stationary Navier-Stokes system by using some classical arguments. This is a joint work with Ch´erif Amrouche (University of Pau and Pays de l’Adour, France).
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