2008 OCT 6 - (VerticalNews.com) -- According to recent research from Changsha, People's Republic of China, "In this paper we explore higher order numerical quadratures for the integration of systems containing Bessel functions. 'two families of methods are presented."

  "One is based on a truncation of the asymptotic series and the other is extending an approach in the work of Levin. The decay of the error drastically improves as frequency grows," wrote S.H. Xiang and colleagues, Central South University ...read more

  2008 OCT 6 - (VerticalNews.com) -- "In this work, a model for the quasistatic frictionless contact between a viscoelastic body with long memory and a foundation is studied. The material constitutive relation is assumed to be nonlinear and the contact is modelled with the normal compliance condition, i.e., the obstacle is assumed deformable," researchers in Spain report.

  "The mechanical damage of the material, caused by excessive stress or strain, is described by the darnage function, which is modelled by a nonlinear partial differential equation. We derive a variational formulation for the problem and prove the existence of its unique weak solution. Then, we introduce a fully discrete scheme for the numerical solutions of the problem, based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, and we obtain error estimates on the approximate solutions," wrote M. Campo and colleagues, University of Santiago ...read more

  2008 OCT 6 - (VerticalNews.com) -- According to recent research from Milan, Italy, "in this paper we aim at controlling physically meaningful quantities with emphasis on environmental applications. This is carried out by an efficient numerical procedure combining the goal-oriented framework [R. Becker, R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods, Acta Numer. 10 (2001) 1-102] with the anisotropic setting introduced in [L. Formaggia, S. Perotto, New anisotropic a priori error estimates, Numer. Math. 89 (2001) 641-6671. ...read more