Publications

• Article dans une revue

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

Colette De Coster, Serge Nicaise

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

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011, 18, pp.769-780. ⟨hal-03721680⟩

• 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

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

Nonlinearity and scaling behavior in a soft lead zirconate titanate piezoceramic

Abdelowahed Hajjaji, Daniel Guyomar, Samira Touhtouh, Sebastien Pruvost, Yahia Boughaleb, Mohamed Rguiti, Christian Courtois, Anne Leriche, Khalil Benkhouja

Lead oxide-based ferroelectrics, represented by lead zirconate titanate [Pb(Zr,Ti)O3] or PZT), are the most widely used materials for piezoelectric actuators, sensors, and transducers due to their excellent piezoelectric properties. Most of these piezoelectric materials are employed under a variety…

Journal of Applied Physics, 2010, 108 (6), ⟨10.1063/1.3486510⟩. ⟨hal-04283059⟩

• Article dans une revue

A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods

Emmanuel Creusé, Serge Nicaise

We consider some (anisotropic and piecewise constant) diffusion problems in domains of R^2, approximated by a discontinuous Galerkin method with polynomials of any fixed degree. We propose an a posteriori error estimator based on gradient recovery by averaging. It is shown that this estimator gives…

Journal of Computational and Applied Mathematics, 2010, 234 (10), pp.2903-2915. ⟨10.1016/j.cam.2010.03.027⟩. ⟨hal-00768641⟩

• Article dans une revue

Depth-sensing indentation modeling for determination of Elastic modulus of thin films

Arnaud Tricoteaux, G. Duarte, Didier Chicot, Éric Le Bourhis, E. Bemporad, J. Lesage

Mechanics of Materials, 2010, 42 (2), pp.166-174. ⟨10.1016/j.mechmat.2009.11.016⟩. ⟨hal-03577752⟩

• Article dans une revue

A remark on the stabilization of the 1-d wave equation, Une remarque sur la stabilisation de l'équation des ondes 1-d

Serge Nicaise, Julie Valein

We consider the wave equation on an interval of length 1 with an interior damping at ξ and with Dirichlet boundary condition at the two ends. It is well-known that, if ξ is rational, the energy does not decay to 0. In this case, we prove that the energy decays exponentially to a constant which we…, Nous considérons l'équation des ondes sur un intervalle de longueur 1 avec un amortissement en un point ξ intérieur et avec la condition au bord de Dirichlet aux deux extrémités. Il est bien-connu que, si ξ est rationnel, l'énergie ne tend pas vers 0. Dans ce cas, nous prouvons que l…

Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2010, 348 (1-2), pp.47-51. ⟨10.1016/j.crma.2009.11.015⟩. ⟨hal-00599639⟩

• Article dans une revue

Quasi exponential decay of a finite difference space discretization of the 1-d wave equation by pointwise interior stabilization

Serge Nicaise, Julie Valein

We consider the wave equation on an interval of length 1 with an interior damping at ξ . It is well-known that this system is well-posed in the energy space and that its natural energy is dissipative. Moreover, as it was proved in Ammari et al. (Asymptot Anal 28(3-4):215-240, 2001), the exponential…

Advances in Computational Mathematics, 2010, 32 (3), pp.303-334. ⟨10.1007/s10444-008-9108-1⟩. ⟨hal-00599626⟩

• Article dans une revue

On the observability of abstract time-discrete linear parabolic equations

Sylvain Ervedoza, Julie Valein

This article aims at analyzing the observability properties of time-discrete approximation schemes of parabolic equations Ż + Az = 0, where A is a self- adjoint positive definite operator with dense domain and compact resolvent. We analyze the observability properties of these diffusive systems for…

Revista Matematica Complutense, 2010, 23 (1), pp.163-190. ⟨10.1007/s13163-009-0014-y⟩. ⟨hal-00599624⟩

• Article dans une revue

Weighted regularization for composite materials in electromagnetism

Patrick Ciarlet, François Lefèvre, Stéphanie Lohrengel, Serge Nicaise

In this paper, a weighted regularization method for the time-harmonic Maxwell equations with perfect conducting or impedance boundary condition in composite materials is presented. The computational domain Ω is the union of polygonal or polyhedral subdomains made of different materials. As a result…

ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (1), pp.75-108. ⟨10.1051/m2an/2009041⟩. ⟨hal-00873065⟩