4,602 research outputs found
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
Surface Geometry of 5D Black Holes and Black Rings
We discuss geometrical properties of the horizon surface of five-dimensional
rotating black holes and black rings. Geometrical invariants characterizing
these 3D geometries are calculated. We obtain a global embedding of the 5D
rotating black horizon surface into a flat space. We also describe the
Kaluza-Klein reduction of the black ring solution (along the direction of its
rotation) which relates this solution to the 4D metric of a static black hole
distorted by the presence of external scalar (dilaton) and vector
(`electromagnetic') field. The properties of the reduced black hole horizon and
its embedding in \E^3 are briefly discussed.Comment: 10 pages, 9 figures, Revtex
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