Finite element solution of Navier Stokes equations adapted to a priori error estimates

The paper is based on qualitative properties of the solution of the Navier-Stokes equations for incompressible fluid, and on properties of their finite element solution. In problems with corner-like singularities (e.g. on the well-known L-shaped domain) usually some adaptive strategy is used. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results.

Industrialization as a key element of sustainable product-service solutions

Product-service systems are seen by many authors to offer potential for significant sustainability benefit. Manufacturing companies are said to be essential to such a change through their influence over product performance and over the use and end-of-life stages. Yet linking these stages such that the producer is incentivized to improve the performance of later stages is still a challenge. This paper argues for placing the producer at the centre of a new arrangement: by seeking to utilize the producer's knowledge of designing and the knowledge of volume production, through creation of platforms, while cooperating closely with other actors. The paper describes three case studies that have used such an approach to design and implement new food production systems. Based on 12 months of action research observations, 10 participating organizations from the cases were studied, and the implemented solutions assessed for environmental, economic and social performance. The results demonstrate a high level of sustainability benefit is achievable using platforms and partners to design product-service systems, while highlighting that changes to production arrangements are necessary but not sufficient to improve whole life-cycle environmental performance of product-service systems, and that producers need to cooperate closely with other actors to achieve the claimed benefits.