Patrick Ciarlet
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View article: Analysis of Time‐Harmonic Electromagnetic Problems With Elliptic Material Coefficients
Analysis of Time‐Harmonic Electromagnetic Problems With Elliptic Material Coefficients Open
We consider time‐harmonic electromagnetic problems with material coefficients represented by elliptic fields, covering a wide range of complex and anisotropic material media. The properties of elliptic fields are analyzed, with particular …
View article: On some coupled local and nonlocal diffusion models
On some coupled local and nonlocal diffusion models Open
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
View article: Explicit T-coercivity for the Stokes problem: A coercive finite element discretization
Explicit T-coercivity for the Stokes problem: A coercive finite element discretization Open
View article: The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="monospace">T</mml:mi></mml:math>-coercivity approach for mixed problems
The -coercivity approach for mixed problems Open
Classically, the well-posedness of variational formulations of mixed linear problems is achieved through the inf-sup condition on the constraint. In this note, we propose an alternative framework to study such problems by using the -coerci…
View article: Multiscale modeling for a class of high-contrast heterogeneous sign-changing problems
Multiscale modeling for a class of high-contrast heterogeneous sign-changing problems Open
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These proble…
View article: Study of a degenerate non-elliptic equation to model plasma heating
Study of a degenerate non-elliptic equation to model plasma heating Open
In this manuscript, we study solutions to resonant Maxwell’s equations in heterogeneous plasmas. We concentrate on the phenomenon of upper-hybrid heating, which occurs in a localized region where electromagnetic waves transfer energy to th…
View article: Crouzeix-Raviart elements on simplicial meshes in $d$ dimensions
Crouzeix-Raviart elements on simplicial meshes in $d$ dimensions Open
In this paper we introduce Crouzeix-Raviart elements of general polynomial order $k$ and spatial dimension $d\geq2$ for simplicial finite element meshes. We give explicit representations of the non-conforming basis functions and prove that…
View article: Adaptive solution of the domain decomposition+<i>L</i><sup>2</sup>-jumps method applied to the neutron diffusion equation on structured meshes
Adaptive solution of the domain decomposition+<i>L</i><sup>2</sup>-jumps method applied to the neutron diffusion equation on structured meshes Open
At the core scale, neutron deterministic calculations are usually based on the neutron diffusion equation. Classically, this equation can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finit…
View article: Thet-Coercivity Approach For Solving Stokes Problem: Stabilization of Finite Element Pairs
Thet-Coercivity Approach For Solving Stokes Problem: Stabilization of Finite Element Pairs Open
View article: References
References Open
View article: Analysis of Time-Harmonic Maxwell Impedance Problems in Anisotropic Media
Analysis of Time-Harmonic Maxwell Impedance Problems in Anisotropic Media Open
International audience
View article: An Optimal Control-Based Numerical Method for Scalar Transmission Problems with Sign-Changing Coefficients
An Optimal Control-Based Numerical Method for Scalar Transmission Problems with Sign-Changing Coefficients Open
International audience
View article: The T-coercivity approach for mixed problems
The T-coercivity approach for mixed problems Open
View article: <i>A posteriori</i> error estimates for mixed finite element discretizations of the Neutron Diffusion equations
<i>A posteriori</i> error estimates for mixed finite element discretizations of the Neutron Diffusion equations Open
We analyse a posteriori error estimates for the discretization of the neutron diffusion equations with mixed finite elements. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion …
View article: On the approximation of electromagnetic fields by edge finite elements—Part 4: analysis of the model with one sign-changing coefficient
On the approximation of electromagnetic fields by edge finite elements—Part 4: analysis of the model with one sign-changing coefficient Open
View article: Notes de cours sur les méthodes variationnelles pour l'analyse et la résolution de problèmes non coercifs
Notes de cours sur les méthodes variationnelles pour l'analyse et la résolution de problèmes non coercifs Open
View article: An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients
An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients Open
In this work, we present a new numerical method for solving the scalar transmission problem with sign-changing coefficients. In electromagnetism, such a transmission problem can occur if the domain of interest is made of a classical dielec…
View article: A Mathematical Study of a Hyperbolic Metamaterial in Free Space
A Mathematical Study of a Hyperbolic Metamaterial in Free Space Open
International audience
View article: Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber
Improvement of hierarchical matrices for 3D elastodynamic problems with a complex wavenumber Open
View article: Limiting amplitude principle and resonances in plasmonic structures with corners: Numerical investigation
Limiting amplitude principle and resonances in plasmonic structures with corners: Numerical investigation Open
View article: ADAPTIVE SOLUTION OF THE NEUTRON DIFFUSION EQUATION WITH HETEROGENEOUS COEFFICIENTS USING THE MIXED FINITE ELEMENT METHOD ON STRUCTURED MESHES
ADAPTIVE SOLUTION OF THE NEUTRON DIFFUSION EQUATION WITH HETEROGENEOUS COEFFICIENTS USING THE MIXED FINITE ELEMENT METHOD ON STRUCTURED MESHES Open
The neutron transport equation can be used to model the physics of the nuclear reactor core. Its solution depends on several variables and requires a lot of high precision computations. One can simplify this model to obtain the SP N equati…
View article: Analysis of Variational Formulations and Low-regularity Solutions for Time-harmonic Electromagnetic Problems in Complex Anisotropic Media
Analysis of Variational Formulations and Low-regularity Solutions for Time-harmonic Electromagnetic Problems in Complex Anisotropic Media Open
International audience
View article: Notes de cours sur les équations de Maxwell et leur approximation
Notes de cours sur les équations de Maxwell et leur approximation Open
View article: Mathematical and numerical analyses for the div-curl and div-curlcurl problems with a sign-changing coefficient
Mathematical and numerical analyses for the div-curl and div-curlcurl problems with a sign-changing coefficient Open
We study the numerical approximation by edge finite elements of fields whose divergence and curl, or divergence and curl-curl, are prescribed in a bounded set $\Omega$ of $\mathbb{R}^3$, together with a boundary condition. Special attentio…
View article: On the efficiency of nested GMRES preconditioners for 3D acoustic and elastodynamic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e3066" altimg="si7.svg"><mml:mi mathvariant="script">H</mml:mi></mml:math>-matrix accelerated Boundary Element Methods
On the efficiency of nested GMRES preconditioners for 3D acoustic and elastodynamic -matrix accelerated Boundary Element Methods Open
View article: Degenerate elliptic equations for resonant wave problems
Degenerate elliptic equations for resonant wave problems Open
The modelling of resonant waves in 2D plasma leads to the coupling of two degenerate elliptic equations with a smooth coefficient $\alpha $ and compact terms. The coefficient $\alpha $ changes sign. The region where $\{\alpha>0\}$ is pr…
View article: On the Approximation of Electromagnetic Fields by Edge Finite Elements. Part 3: Sensitivity to Coefficients
On the Approximation of Electromagnetic Fields by Edge Finite Elements. Part 3: Sensitivity to Coefficients Open
International audience
View article: On the approximation of electromagnetic fields by edge finite elements. Part 3: sensitivity to coefficients
On the approximation of electromagnetic fields by edge finite elements. Part 3: sensitivity to coefficients Open
View article: A variational formulation for coupled degenerate elliptic equations with different signs
A variational formulation for coupled degenerate elliptic equations with different signs Open
We study a coupling of two degenerate elliptic equations in 2D with a smooth sign changing coefficient and compact terms. The degeneracy of the coefficient is critical with respect to the theory of weighted Sobolev spaces. An adapted funct…
View article: On the Convergence in $H^1$-Norm for the Fractional Laplacian
On the Convergence in $H^1$-Norm for the Fractional Laplacian Open
We consider the numerical solution of the fractional Laplacian of index $s\in(1/2,1)$ in a bounded domain $Ω$ with homogeneous boundary conditions. Its solution a priori belongs to the fractional order Sobolev space ${\widetilde H}^s(Ω)$. …