Abstract

International audience Industrial development can generate hazardous situations – in particular, when there is a need to deal with dangerous substances, such as those in chemical or petrochemical plants. Too often, these industries are located in the heart of urbanized areas with high-density populations, as urbanization intrudes on the hazardous sites (originally established outside of cities). Protecting civil populations from these risks – either through precautionary measures or special crisis management plans, if a catastrophe occurs – is a key issue. To better protect citizens, identifying the risks to which they are exposed and also how they perceive the risks in their area can help authorities and stakeholders better understand the risks (Glatron & Beck, 2008). Adequate knowledge of these risks can also dissuade populations from settling in certain zones and thus lower their vulnerability. Finally, authorities need to assess the exposure of populations to hazards – through modelling – to set up appropriate and efficient risk management plans based on land planning. The present chapter – founded on responses to a questionnaire-based investigation (see the Annex) carried out in the Milazzo–Valle del Mela area of Sicily, in 2008 – explores two main aspects of exposure assessment: space-time-pattern methodological challenges and results of individual space-time activity data extracted from the investigation in the Milazzo–Valle del Mela area. Document type: Part of book or chapter of book

Abstract

We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise polynomials of this space-time variational formulation require a CFL condition to ensure stability. To overcome this restriction in the case of piecewise multilinear, continuous ansatz and test functions, a stabilisation is well-known, which leads to an unconditionally stable space-time finite element method. In this work, we generalise this stabilisation idea from the lowestorder case to the higher-order case, i.e. to an arbitrary polynomial degree. We give numerical examples for a one-dimensional spatial domain, where the unconditional stability and optimal convergence rates in space-time norms are illustrated.