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We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of Itô type. This is then used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochastic evolution problems in Hilbert space. Finally, this abstract theory is applied to the linear heat and wave… (More)

- Stig Larsson, Vidar Thomée
- 2003

Preface Our purpose in this book is to give an elementary, relatively short, and hopefully readable account of the basic types of linear partial differential equations and their properties, together with the most commonly used methods for their numerical solution. Our approach is to integrate the mathematical analysis of the differential equations with the… (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)

Technology transfer, and thus industry-relevant research, involves more than merely producing research results and delivering them in publications and technical reports. It demands close cooperation and collaboration between industry and academia throughout the entire research process. During research conducted in a partnership between Blekinge Institute of… (More)

- Stig Larsson
- 1999

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)

- M Crouzeix, S Larsson, V Thom, Ee
- 1994

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)

The process of component- and component-based system development differs in many significant ways from the "classical" development process of software systems. The main difference is in the separation of the development process of components from the development process of systems. This fact has a significant impact on the development process. Since the… (More)

Developing the right products the right way is challenging, not least in software product development. It requires sound business decisions as well as good engineering practices. Various software development life-cycle models can be mapped to business decision models by mapping business decision gates and major development milestones. Two well-known… (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)