Learn More
The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based(More)
In these lectures I discuss error analysis techniques for nite element methods for systems of reaction-diiusion equations with applications in dynamical systems theory. The emphasis is on pedagogical aspects and analysis techniques rather than on results. The list of techniques discussed include: analytic semigroup, parabolic smoothing, non-smooth data(More)
We prove the analyticity (uniform in h) of the semigroups generated on Lp(0;1), 1 p 1, by nite element analogues A h of a one-dimensional second order elliptic operator A under Dirichlet boundary conditions. This is accomplished by showing the appropriate estimates for the resolvents by means of energy arguments. The results are applied to prove stability(More)
In recent years component-based development has in resent years become an established approach. Component-based Software Engineering (CBSE) that deals with the entire lifecycle of component-based products has been focused on technologies related to design and implementation of software components and systems built from software components. The experience(More)
Software development life-cycle models and business decision models contribute to the control of product development in different ways. However, both kinds of models have limitations. SDLMs do not ensure that resources are used in the right projects, that the market is available, or that the organization is ready for a release. Similarly, business decision(More)
Software product line engineering has emerged as one of the dominant paradigms for developing variety of software products based on a shared platform and shared software artifacts. An important and challenging type of software maintenance and evolution is how to cost-effectively manage the migration of legacy systems towards product lines. This paper(More)
Semidiscrete finite element approximation of the linear stochastic wave equation with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies(More)