Numerical Methods for Non-Stationary Stokes Flow

We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, where the unknown source densities of the latter can be determined from uniquely solvable boundary integral equations’ systems. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is used. Some simulations of a model problem are carried out and illustrate the efficiency of the method.

Finding Spaces for Urban Food Production – Matching Spatial and Stakeholder Analysis with Urban Agriculture Approaches in the Urban Renewal Area of Dortmund-Hörde, Germany

Using the case of an economically declined neighbourhood in the post-industrial German Ruhr Area (sometimes characterized as Germany’s “Rust Belt”), we analyse, describe and conclude how urban agriculture can be used as a catalyst to stimulate and support urban renewal and regeneration, especially from a socio-cultural perspective. Using the methodological framework of participatory action research, and linking bottom-up and top-down planning approaches, a project path was developed to include the population affected and foster individual responsibility for their district, as well as to strengthen inhabitants and stakeholder groups in a permanent collective stewardship for the individual forms of urban agriculture developed and implemented. On a more abstract level, the research carried out can be characterized as a form of action research with an intended transgression of the boundaries between research, planning, design, and implementation. We conclude that by synchronously combining those four domains with intense feedback loops, synergies for the academic knowledge on the potential performance of urban agriculture in terms of sustainable development, as well as the benefits for the case-study area and the interests of individual urban gardeners can be achieved.