We consider a fully discrete approximation of the H gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an implicit Euler time discretization. The numerical method is shown to be stable and to exhibit optimal ...

Under fatigue-loading, short-fiber reinforced thermoplastic materials typically show a progressive degradation of the stiffness tensor. The prior to failure is primary interest from an engineering perspective, as it determines when fatigue cracks nucleate. Efficient modeling this stage allows engineer monitor fatigue-process and design criteria which ensure safe application component under inve...

This paper extends for the first time Schaback’s linear discretization theory to nonlinear operator equations, relying heavily on the methods in Böhmer’s 2010 book. There is no restriction to elliptic problems or to symmetric numerical methods like Galerkin techniques. Trial spaces can be arbitrary, including spectral and meshless methods, but have to approximate the solution well, and testing ...

We construct two discretizations of dense time automata which generate the same untimed language as the dense time automata.

In the data-mining field, many learning methods — such as association rules, Bayesian networks, and induction rules (Grzymala-Busse & Stefanowski, 2001) — can handle only discrete attributes. Therefore, before the machine-learning process, it is necessary to re-encode each continuous attribute in a discrete attribute constituted by a set of intervals. For example, the age attribute can be trans...

A redesign method for discretizing a continuous-time controller is proposed. The resulting hybrid control system, for example with continuous-time plant and discrete-time controller, is stable, and performance including the system's inter-sampling behaviour can be optimized by approximating some chosen reference transfer function of the continuous-time control system. In order to obtain a tract...