Single-Grid Spectral Collocation for the Navier-Stokes Equations

The aim of the paper is to study a collocation spectral methodto approximate the Navier-Stokes equations: only one grid isused, which is built from the nodes of a Gauss-Lobatto quadratureformula, either of Legendre or of Chebyshev type. The convergenceis proved for the Stokes problem provided with inhomogeneusDirichlet conditions, then thoroughly analysed for the Navier-Stokesequations. The practical implementation algorithm is presented,together with numerical results.     

SENSITIVITY OF DARCY’S LAWTO DISCONTINUITIES

The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient K of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of K.The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.     

A Mixed Method for the Time-Dependent Navier-Stokes Problem

We study a spatial discretization of the time-dependent Navier-Stokesproblem by a mixed finite-element method where the incompressibilitycondition is exactly satisfied, the unknowns being the streamfunction and the vorticity. Optimal error estimates are derived.     

ChemInform Abstract: XeNO3+: A Gaseous Cation Characterized by a Remarkably Strong Xe—O Bond.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

The Rain on Underground Porous Media Part I: Analysis of a Richards Model

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.