Adel Blouza

Nagdhi's Shell Model: Existence, Uniqueness and Continuous Dependence on the Midsurface

In this work, we present a new formulation for Nagdhis model for shells with little regularity. This formulation allows for existence and uniqueness for general shells with discontinuous curvatures. We show that it coincides with the classical formulation when both are valid. We furthermore establish the continuous dependence of the solution to Nagdhis problem on the midsurface.

PARALLEL IN TIME ALGORITHMS WITH REDUCTION METHODS FOR SOLVING CHEMICAL KINETICS

We design suitable parallel in time algorithms coupled with reduction methods for the stiff differential systems integration arising in chemical kinetics. We consider linear as well as nonlinear systems. Numerical efficiency of our approach is illustrated by a realistic ozone production model.

An Up-to-the Boundary Version of Friedrichs's Lemma and Applications to the Linear Koiter Shell Model

In this work, we introduce a variant of the standard mollifier technique that is valid up to the boundary of a Lipschitz domain in

Reduction of linear kinetic systems with multiple scales

\mathbb{R}^n

A posteriori analysis of penalized and mixed formulations of Koiter's shell model

. A version of Friedrichss lemma is derived that gives an estimate up to the boundary for the commutator of the multiplication by a Lipschitz function and the modified mollification. We use this version of Friedrichss lemma to prove the density of smooth functions in the new function space introduced in our earlierwork concerning the linear Koiter shell model for shells with little regularity. The density of smooth functions is in turn used to prove continuous dependence of the solution of Koiters model on the midsurface. This provides a complete justification of our new formulation of the Koiter model.

Spectral Discretization of a Naghdi Shell Model

We present a simple and general reduction algorithm for stiff monomolecular kinetic systems. The reduction is based on algebraic techniques and consists in eliminating the fastest dynamics in the initial system without any change of basis. This process is systematic and is not based on chemical conventional assumptions or on singular perturbation techniques. Systems can be reduced even if they are not in the Tikhonov form. This reduction process is applied to kinetic systems with kinetic constants belonging to different scales. Error estimates for all species are given. Numerical tests are performed. §Part of this work was carried out during the 1997-1998 year at the Department of Mathematics at MIT, USA.

The Rain on Underground Porous Media

We are interested in finite element approximations of a Koiter model for linearly elastic shells with little regularity. To perform conforming method, we present a penalized and a mixed formulations of the model allowing to approximate and to enforce weakly mechanical constraints, respectively. We establish existence and uniqueness of the solution to the both formulations. Moreover, a posteriori analysis is led yielding an upper bound and a lower bound of the error. Finally, numerical results are presented to illustrate the efficiency of the a posteriori estimators. We therefore, propose a mesh adaptivity strategy relying on these indicators.

Existence and uniqueness for the linear Koiter model for shells with little regularity

We consider the Naghdi equations which model a thin three-dimensional shell. We propose a spectral discretization of this problem in the case where the midsurface of the shell is weakly regular. We perform the numerical analysis of the discrete problem and prove optimal error estimates.

Existence et unicité pour le modèle de Koiter pour une coque peu régulière

The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.