Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory

Guiding principles for the development and application of solid-phase phosphorus adsorbents for freshwater ecosystems

While a diverse array of phosphorus (P)-adsorbent materials is currently available for application to freshwater aquatic systems, selection of the most appropriate P-adsorbents remains problematic. In particular, there has to be a close correspondence between attributes of the P-adsorbent, its field performance, and the management goals for treatment. These management goals may vary from a rapid reduction in dissolved P to address seasonal enrichments from internal loading, targeting external fluxes due to anthropogenic sources, or long term inactivation of internal P inventories contained within bottom sediments. It also remains a challenge to develop new methods and materials that are ecologically benign and cost-effective. We draw on evidence in the literature and the authors’ personal experiences in the field, to summarise the attributes of a range of P-adsorbent materials. We offer 'guiding principles' to support practical use of existing materials and outline key development needs for new materials