Publications

• Article dans une revue

Residual a posteriori error estimators for contact problems in elasticity

Patrick Hild, Serge Nicaise

This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for…

ESAIM: Mathematical Modelling and Numerical Analysis, 2007, 41 (5), pp.897-923. ⟨10.1051/m2an:2007045⟩. ⟨hal-00466479⟩

• Article dans une revue

Raw materials dossier, Dossier matières premières

Didier Bernache-Assollant, Jean-Pierre Bonnet, C. Carry, C. Chaput., Thierry Chartier, J.-L. Chermant, B. Durand, S. Garrault, N. Herlin, J.-M. Lamerant, Y. Leconte, S. Le Gallet, Anne Leriche, J.-C. Niepce, J. Poirier, F. Rebillat, F. Valdivieso

Industrie céramique et verrière (L’), 2007, 1012, pp.40-73. ⟨hal-00293786⟩

• Article dans une revue

A discontinuous Galerkin method on refined meshes for the 2D time-harmonic Maxwell equations in composite materials

Stephanie Lohrengel, Serge Nicaise

In this paper, a discontinuous Galerkin method for the two-dimensional time-harmonic Maxwell equations in composite materials is presented. The divergence constraint is taken into account by a regularized variational formulation and the tangential and normal jumps of the discrete solution at the…

Journal of Computational and Applied Mathematics, 2007, 206 (1), pp.27-54. ⟨10.1016/j.cam.2006.05.020⟩. ⟨hal-00210426⟩

• Article dans une revue

Weak Solutions of Semilinear PDEs in Sobolev Spaces and Their Probabilistic Interpretation via the FBSDEs

Isabelle Massa-Turpin, Youssef Ouknine, Isabelle Turpin

The article is devoted to representation of weak solutions (in Sobolev sense) of degenerate parabolic partial differential equations through forward-backward stochastic differential equations. Before, we prove a weak version of a norm equivalence result.

Stochastic Analysis and Applications, 2006, 24 (4), pp.871-888. ⟨10.1080/07362990600753601⟩. ⟨hal-03359278⟩

• Thèse

Dual mixed finite element method of the elasticity and elastodynamic problems: a priori and a posteriori error analysis., Méthode des éléments finis mixte duale pour les problèmes de l'élasticité et de l'élastodynamique: analyse d'erreur à priori et à posteriori.

Lahcen Boulaajine

In this work, we study the refinement of grids for the dual mixed finite element method for two types of problems: the first one concerns the linear elasticity problem and the second one the linear elastodynamic problem. For these two types of problems and in nonregular domains, the mixed finite…, Dans ce travail, nous étudions le raffinement de maillage pour des méthodes d'éléments finis mixtes duales pour deux types de problèmes : le premier concerne le problème de l'élasticité linéaire et le second problème celui de l'élastodynamique. Pour ces deux types de problèmes et…

Mathematics [math]. Université de Valenciennes et du Hainaut-Cambresis, 2006. English. ⟨NNT : ⟩. ⟨tel-00136422⟩

• Article dans une revue

Elaboration of nitride thin films by reactive sputtering

Pierre Yves Jouan, Arnaud Tricoteaux, Nicolas Horny

The aim of this paper is first a better understanding of DC reactive magnetron sputtering and its implications, such as the hysteresis effect and the process instability. In a second part, this article is devoted to an example of specific application: Aluminium Nitride. AlN thin films have been…, O objetivo desse artigo, em um primeiro momento, é uma melhor compreensão da vaporização em um ambiente magnetron reativo DC e as suas conseqüências, tais como o efeito da histeresis e o processo de instabilidade. A segunda parte desse trabalho está dedicada a um estudo de caso: o nitreto de…

Rem : Revista Escola de Minas, 2006, 59 (2), pp.225-232. ⟨10.1590/s0370-44672006000200013⟩. ⟨hal-03455040⟩

• Article dans une revue

Segmentation of complex geophysical structures with well data

Christian Gout, Carole Le Guyader

In many problems of geophysical interest, when trying to segment images (i.e., to locate interfaces between different regions on the images), one has to deal with data that exhibit very complex structures. This occurs, for instance, when describing complex geophysical images (with layers, faults…

Computational Geosciences, 2006, 10 (4), pp.363-372. ⟨10.1007/s10596-006-9029-3⟩. ⟨hal-01024268⟩

• Article dans une revue

Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Emmanuel Creusé, Serge Nicaise

In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is…

ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (2), pp.413-430. ⟨10.1051/m2an:2006017⟩. ⟨hal-00768645⟩

• Article dans une revue

Anisotropic a posteriori error estimation for the mixed discontinuous Galerkin approximation of the Stokes problem

Emmanuel Creusé, Serge Nicaise

The paper presents a posteriori error estimates for the mixed discontinuous Galerkin approximation of the stationary Stokes problem. We consider anisotropic finite element discretizations, i.e. elements with very large aspect ratio. Our analysis covers two- and three-dimensional domains. Lower and…

Numerical Methods for Partial Differential Equations, 2006, 22 (2), ⟨10.1002/num.20107⟩. ⟨hal-00768690⟩

• Article dans une revue

Isotropic and anisotropic error estimation of the mixed finite element method for second order operators in divergence form

Serge Nicaise, Emmanuel Creusé

This paper presents an a posteriori residual error estimator for the mixed FEM of second order operators using isotropic or anisotropic meshes in $R^d$, $d$=2 or 3. The reliability and efficiency of our estimator is established without any regularity assumptions on the solution of our problem.

Electronic Transactions on Numerical Analysis, 2006, 23, pp.38-62. ⟨hal-00768689⟩