Stabilized Finite Element Methods

We give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection-diffusion equation.Ope

Stabilized finite element methods : I. application to the advective-diffusive model

Projet MODULE

A relationship between stabilized finite element methods and the Galerkin method with bubble functions

Projet MENUSINRésumé disponible dans le fichier PD

Unified model of baryonic matter and dark components

We investigate an interacting two-fluid cosmological model and introduce a scalar field representation by means of a linear combination of the individual energy densities. Applying the integrability condition to the scalar field equation we show that this "exotic quintessence" is driven by an exponential potential and the two-fluid mixture can be considered as a model of three components. These components are associated with baryonic matter, dark matter and dark energy respectively. We use the Simon, Verde & Jimenez (2005) determination of the redshift dependence of the Hubble parameter to constrain the current density parameters of this model. With the best fit density parameters we obtain the transition redshift between non accelerated and accelerated regimes z_{acc}=0.66 and the time elapsed since the initial singularity t_0= 19.8 Gyr. We study the perturbation evolution of this model and find that the energy density perturbation decreases with the cosmological time.Comment: 8 pages, 6 figures A new section adde

Astronomical Distance Determination in the Space Age: Secondary Distance Indicators

The formal division of the distance indicators into primary and secondary leads to difficulties in description of methods which can actually be used in two ways: with, and without the support of the other methods for scaling. Thus instead of concentrating on the scaling requirement we concentrate on all methods of distance determination to extragalactic sources which are designated, at least formally, to use for individual sources. Among those, the Supernovae Ia is clearly the leader due to its enormous success in determination of the expansion rate of the Universe. However, new methods are rapidly developing, and there is also a progress in more traditional methods. We give a general overview of the methods but we mostly concentrate on the most recent developments in each field, and future expectations. © 2018, The Author(s)