We present here a theoretical study of eigenmodes inaxisymmetric elastic layers.The mathematical modelling allows us to bring this problem to a spectral studyof a sequence of unbounded self-adjoint operators A n , $n\in \mathbb{N}$ , in a suitableHilbert space. We show that the essential spectrum of A n is an interval oftype $[\gamma,+\infty[$ and that, under certain conditions on the coefficientsof the medium, the discrete spectrum is non empty.

This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al. The new model itself suggests an implicit time-discretization which is combined with thefinite element method in space. A priori error estimates are established for the quasioptimal spatial approximation of the stress fieldwithin one time-step. A posteriorierror estimates motivate an adaptive mesh-refining algorithm for efficient discretization. The proposed scheme enables numerical simulations which show that the model allows for hysteresis.

In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B modelwithout convective terms is considered. Assuming the domain to be a convexpolygon, existence of a solutionis proved for small relaxation times.Continuous piecewise linear finite elements together witha Galerkin Least Square (GLS) method are studied for solving this problem.Existence and a priori error estimatesare established using a Newton-chord fixed point theorem,a posteriori error estimates are also derived.An Elastic Viscous Split Stress (EVSS) scheme related to the GLS methodis introduced. Numerical results confirm the theoretical predictions.

We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.

The paper deals with some mixed finite element methods on a classof anisotropic meshes based on tetrahedra and prismatic (pentahedral)elements. Anisotropic localinterpolation error estimates are derived in some anisotropic weighted Sobolevspaces. As particularapplications, the numerical approximation by mixed methods of the Laplace equationin domainswith edges is investigated where anisotropic finiteelement meshes are appropriate. Optimal error estimates are obtained using some anisotropic regularity results of thesolutions.

In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfyan affine boundary condition in the second lamination convex hull of the wells of the functional.

The aim of this article is to give a regularization method for an unilateral obstacle problem with obstacle ψ and second member f, which generalizes the one established by the authors of [4] in case of null obstacle and a second member is equal to constant 1.

We semi-discretize in space a time-dependent Navier-Stokes systemon a three-dimensional polyhedron by finite-elements schemesdefined on two grids. In the first step, the fully non-linearproblem is semi-discretized on a coarse grid, with mesh-size H.In the second step, the problem is linearized by substitutinginto the non-linear term, the velocity u H computed at stepone, and the linearized problem is semi-discretized on a finegrid with mesh-size h. This approach is motivated by the factthat, on a convex polyhedron and under adequate assumptions on thedata, the contribution of u H to the error analysis ismeasured in the L 2 norm in space and time, and thus, for thelowest-degree elements, is of the order of H 2. Hence, an errorof the order of h can be recovered at the second step, providedh = H 2.

A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.