Naima Debit

Naima Debit
Claude Bernard University Lyon 1 | UCBL · Institut Camille Jordan (ICJ)

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29
Publications
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262
Citations

Publications

Publications (29)
Article
Full-text available
We are interested in recovering boundary data in a dispersive oxygen-balance model. The missing boundary condition is the flux of the biochemical oxygen demand (the amount of oxygen necessary for the oxidation of organic matter) at one extreme point. The observations are collected on the dissolved oxygen at the other extremity. This problem turns o...
Article
This paper is concerned with solving Cauchy problem for parabolic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to an adapted stopping criteria depending on nois...
Article
Full-text available
In this paper, we derive an a posteriori error estimator, for nonconforming finite element approximation of convection-diffusion equation. The a posteriori error estimator is based on the local problems on stars. Finally, we prove the reliability and the efficiency of the estimator without saturation assumption nor comparison with residual estimato...
Article
Full-text available
We give an a posteriori error estimator for low order nonconforming finite element approximations of diffusion-reaction and Stokes problems, which relies on the solution of local problems on stars. It is proved to be equivalent to the energy error up to a data oscillation, without requiring Helmholtz decomposition of the error nor saturation assump...
Article
This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimi...
Article
We consider anisotropic adaptive methods based on a metric related to the Hessian of the solution. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Ω of R d ,d≥2. We also present an algorithm gen...
Article
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The paper deals with the existence and uniqueness of solutions of some non linear parabolic inequalities in the Orlicz-Sobolev spaces framework.
Article
A conservative method to solve waste repository problems with non-standard interface conditions is presented. One hereby obtains a coupled system, in which all matching conditions remain implicit. A numerical scheme is proposed and stability analysis as well as error estimates are provided.
Article
Full-text available
A variational approach to derive a piecewise constant conservative approximation of anisotropic diffusion equations is presented. A priori error estimates are derived assuming usual mesh regularity constraints and a posteriori error indicator is proposed and analyzed for the model problem.
Article
Full-text available
this paper either finite element or spectral element versions of the method. The solution is discontinuous on the interface, and the matching is implicitly contained in the equations formulation. The main characteristics of the approach we introduce can be summarized as: ffl Flexibility on the choice of discretizations on each subdomain; ffl No glo...
Article
A non-standard Equilibrium Method to solve some elliptic problems with non-standard boundary conditions is presented. A conforming primal variational formulation is used on the boundary, whereas an equilibrium one is established on the domain. One hereby obtains a coupled system, in which all matching conditions remain implicit. Existence and uniqu...
Article
A new space–time domain decomposition method (STDDM) is presented. The space–time domain is partitioned in subdomains, and different discretizations are used in each space–time subdomain. Time-integration in space–time variational methods is derived in a different manner from what has been presented so far–it is contained in the time-discontinuous...
Article
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares; a finite element approximation is used on the first square and a spectral discretization is used on the second. Two kinds of matching conditions on the interface are presented and compared; in both cases, error estimates are proved.
Article
The aim of spectral element methods is to combine the relative advantages of finite elements (complex geometries) and spectral techniques (high accuracy). We present here a new non-conforming method which allows for greater flexibility in spectral element domain decomposition, as well as direct spectral element-finite element coupling. Theoretical...
Article
In this paper we propose and analyze the extension of the mortar element method to the numerical approximation of the Stokes equation. The aim is to allow a domain decomposition technique with either a spectral or a finite element discretization in each subdomain. The mortar element framework is shown to provide here also an optimal resolution, fro...
Article
Full-text available
This paper is concerned with solving Cauchy problem for elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, Cauchy problem is presented as an optimal control problem. Numerical convergence analysis is carried out and leads to an adapted stopping criteri...

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