Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data

In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2

Simultaneous expansion and rotation of shear-free universes in modified gravity

We show in a fully covariant way that, there exist a class of $f(R)$ models for which a shear-free, almost FLRW universe can expand and rotate at the same time .Comment: 4 pages, no figures. Contribution submitted to the proceedings of the Spanish Relativity Meeting ERE2011, September 2011, Madrid, Spai

A new approach to reconstruction methods in f(R)f(R) gravity

We present a new approach of the reconstruction method based on the use of the cosmic parameters instead of a time law for the scale factor. This allows the derivation and analysis of a set of new non-trivial cosmological solutions for $f(R)$-gravity. A number of simple examples are given.Comment: 5 pages, Revtex