Several a posteriori error estimates for the Stokes equations have been derived by several authors. In this paper we compare some estimates based on the solution of local Stokes systems with estimates based on the residuals of the discretized finite element equations. Their performance as local indicators as well as global estimates is investigated.
We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are… (More)
One of the conditions in the Kreiss matrix theorem involves the resolvent of the matrices A under consideration. This so-called resolvent condition is known to imply, for all n ≥ 1, the upper bounds A n ≤ eK(N + 1) and A n ≤ eK(n + 1). Here · · is the spectral norm, K is the constant occurring in the resolvent condition, and the order of A is equal to N + 1… (More)
We describe the derivation of order conditions, without restrictions on stage order, for general linear methods for ordinary differential equations. This derivation is based on the extension of Albrecht approach proposed in the context of Runge-Kutta and composite and linear cyclic methods. This approach was generalized by Jackiewicz and Tracogna to… (More)