Publications

• Article dans une revue

Exponential stability of the wave equation with boundary time-varying delay

Serge Nicaise, Cristina Pignotti, Julie Valein

We consider the wave equation with a time-varying delay term in the boundary condition in a bounded and smooth domain [\Omega\subset\RR^n.] Under suitable assumptions, we prove exponential stability of the solution. These results are obtained by introducing suitable energies and suitable Lyapunov…

Discrete and Continuous Dynamical Systems - Series S, 2011, 4 (3), pp.693-722. ⟨10.3934/dcdss.2011.4.693⟩. ⟨hal-00599629⟩

• Communication dans un congrès

Des courbes et surfaces " Bézier " Une histoire de géométrie polaire brûlante d'actualité.

Jean-Paul Becar, Jean Vareille

XVIIème colloque national de la recherche en IUT, CNRIUT'11., Jun 2011, Cherbourg, France. ⟨hal-00662745⟩

• Rapport

An hp Finite Element Method for singularly perturbed transmission problems in smooth domains

Serge Nicaise, Xenophontos Christos

We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high and interface layers along…

2011. ⟨hal-00583134⟩

• Rapport

Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks

Serge Nicaise

A Mindlin-Timoshenko model with non constant and non smooth coefficients set in a bounded domain of $\R^d, d\geq 1$ with some internal dissipations is proposed. It corresponds to the coupling between the wave equation and the dynamical elastic system. If the dissipation acts on both equations, we…

2011. ⟨hal-00566157⟩

• Pré-publication, Document de travail

Time-domain study of the Drude-Born-Fedorov model for a class of heterogeneous chiral materials

Patrick Ciarlet, Guillaume Legendre, Serge Nicaise

We deal with the well-posedness of the transient Maxwell equations in a particular class of heterogeneous chiral material modeled by the Drude-Born-Fedorov constitutive relations. A new formulation of the underlying evolution problem allows us to correct a previous result establishing the existence…

2011. ⟨hal-00430196v2⟩

• Article dans une revue

An extended finite element method for 2D edge elements

Stephanie Lohrengel, François Lefèvre, Serge Nicaise

A new extended Finite Element Method based on two-dimensional edge elements is presented and applied to solve the time-harmonic Maxwell equations in domains with cracks. Error analysis is performed and shows the method to be convergent with an order of at least O(h1/2-η). The implementation of the…

International Journal of Numerical Analysis and Modeling, 2011, 8 (4), pp.641-645. ⟨hal-01888373⟩

• Article dans une revue

Optimal convergence analysis for the extended finite element method

Serge Nicaise, Yves Renard, Elie Chahine

We establish some optimal a priori error estimate on some variants of the eXtended Finite Element Method (Xfem), namely the Xfem with a cut-off function and the standard Xfem with a fixed enrichment area. The results are established for the Lame system (homogeneous isotropic elasticity) and the…

International Journal for Numerical Methods in Engineering, 2011, 86, pp.528-548. ⟨10.1002/nme.3092⟩. ⟨hal-00339853v2⟩

• Article dans une revue

Singular behavior of the solution of the Helmholtz equation in weighted L^p -Sobolev spaces

Colette De Coster, Serge Nicaise

We study the Helmholtz equation − ∆u + zu = g in Ω, with Dirichlet boundary conditions in a polygonal domain Ω, where z is a complex number. Here g belongs to L^p_µ (Ω) = {v ∈ L^p_loc (Ω) : r^µ v ∈ L^p (Ω)}, with a real parameter µ and r(x) the distance from x to the set of corners of Ω. We give…

Advances in Differential Equations, 2011, 16, pp.165-198. ⟨hal-03721687⟩

• Article dans une revue

Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction

David Dereudre, Frédéric Lavancier

General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be subjected to a geometric hardcore interaction,…

Computational Statistics and Data Analysis, 2011, 55 (1), pp.498-519. ⟨10.1016/j.csda.2010.05.018⟩. ⟨hal-00402029v2⟩

• Article dans une revue

Singular behavior of the solution of the periodic-Dirichlet heat equation in weighted L^p -Sobolev spaces

Colette De Coster, Serge Nicaise

We consider the heat equation in a polygonal domain Ω of the plane in weighted L^p-Sobolev spaces ∂_t u − ∆u = h, in Ω × ] − π, π[, u = 0, on ∂Ω × [−π, π], u(•, −π) = u(•, π), in Ω. Here h belongs to L^p (−π, π; L^p_µ (Ω)), where L^p_µ (Ω) = {v ∈ L^p_loc (Ω) : r^µ v ∈ L p (Ω)}, with a real…

Advances in Differential Equations, 2011, 16, pp.221-256. ⟨hal-03721684⟩