The local projection method is applied to inf-sup stable discretisations of the Oseen problem. Error bounds of order r are proven for known inf-sup stable pairs of finite element spaces which approximate velocity and pressure by elements of order r and r− 1, respectively. In case of a positive reaction coefficient, the error constants are robust with respect to the viscosity but depend on the p...

We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

o enhance the performances of rough-neural networks (R-NNs) in the system identification‎, ‎on the base of emotional learning‎, ‎a new stable learning algorithm is developed for them‎. ‎This algorithm facilitates the error convergence by increasing the memory depth of R-NNs‎. ‎To this end‎, ‎an emotional signal as a linear combination of identification error and its differences is used to achie...

We study the macroscopic scaling and weak coupling limit for a random Schrödinger equation on Z. We prove that the Wigner transforms of a large class of ”macroscopic” solutions converge in r-th mean to solutions of a linear Boltzmann equation, for any finite value of r ∈ R+. This extends previous results where convergence in expectation was established.

A modi ed nite di erence approximation for interface problems in R n is presented The essence of the modi cation falls in the simultaneous discretization of any two normal components of the ux at the opposite faces of the nite volume In this way the continuous normal component of the ux through an interface is approximated by nite di erences with second order consistency The derived scheme has ...

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

New deferred correction methods for the numerical solution of initial value problems in ordinary differential equations have recently been introduced by Dutt, Greengard and Rokhlin. A convergence proof is presented for these methods, based on the abstract Stetter-Lindberg-Skeel framework and Spijker-type norms. It is shown that p corrections of an order-r one-step solver yield order r(p+ 1) acc...