Publications

• 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⟩

• 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⟩

• 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 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⟩

• Article dans une revue

Quadratic functors on pointed categories

Manfred Hartl, Christine Vespa

We study polynomial functors of degree $2$, called quadratic, with values in the category of abelian groups $Ab$, and whose source category is an arbitrary category $\C$ with null object such that all objects are colimits of copies of a generating object $E$ which is small and regular projective;…

Advances in Mathematics, 2011, 226 (5), pp.3927-4010. ⟨10.1016/j.aim.2010.11.008⟩. ⟨hal-00334292v3⟩

• Article dans une revue

Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system

Emmanuel Creusé, Serge Nicaise, Emmanuel Verhille

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div ) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up…

Calcolo, 2011, 48 (4), pp.307-335. ⟨10.1007/s10092-011-0042-0⟩. ⟨hal-00531654⟩