Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators

We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

In Llanas and Lantarón, J. Sci. Comput. 46, 485–518 (2011) we proposed an algorithm (EDAS-d) to approximate the jump discontinuity set of functions defined on subsets of ℝ d . This procedure is based on adaptive splitting of the domain of the function guided by the value of an average integral. The above study was limited to the 1D and 2D versions of the algorithm. In this paper we address the three-dimensional problem. We prove an integral inequality (in the case d=3) which constitutes the basis of EDAS-3. We have performed detailed computational experiments demonstrating effective edge detection in 3D function models with different interface topologies. EDAS-1 and EDAS-2 appealing properties are extensible to the 3D cas

Early‐season mass‐flowering crop cover dilutes wild bee abundance and species richness in temperate regions: A quantitative synthesis

Pollinators benefit from increasing floral resources in agricultural landscapes, which could be an underexplored co‐benefit of mass‐flowering crop cultivation. However, the impacts of mass‐flowering crops on pollinator communities are complex and appear to be context‐dependent, mediated by factors such as crop flowering time and the availability of other flower resources in the landscape. A synthesis of research is needed to develop management recommendations for effective pollinator conservation in agroecosystems. By combining 22 datasets from 13 publications conducted in nine temperate countries (20 European, 2 North American), we investigated if mass‐flowering crop flowering time (early or late season), bloom state (during or after crop flowering) and extent of non‐crop habitat cover in the landscape moderated the effect of mass‐flowering crop cover on wild pollinator abundance and species richness in mass‐flowering crop and non‐crop habitats. During bloom, wild bee abundance and richness are negatively related to mass‐flowering crop cover. Dilution effects were predominant in crop habitats and early in the season, except for bumblebees, which declined with mass‐flowering crop cover irrespective of habitat or season. Late in the season and in non‐crop habitats, several of these negative relationships were either absent or reversed. Late‐season mass‐flowering crop cover is positively related to honeybee abundance in crop habitats and to other bee abundance in non‐crop habitats. These results indicate that crop‐adapted species, like honeybees, move to forage and concentrate on late‐season mass‐flowering crops at a time when flower availability in the landscape is limited, potentially alleviating competition for flower resources in non‐crop habitats. We found no evidence of pollinators moving from mass‐flowering crop to non‐crop habitats after crop bloom. Synthesis and applications: Our results confirm that increasing early‐season mass‐flowering crop cover dilutes wild pollinators in crop habitats during bloom. We find that dilution effects were absent late in the season. While mass‐flowering crop cultivation alone is unlikely to be sufficient for maintaining pollinators, as part of carefully designed diverse crop rotations or mixtures combined with the preservation of permanent non‐crop habitats, it might provide valuable supplementary food resources for pollinators in temperate agroecosystems, particularly later in the season when alternative flower resources are scarce

Wild insect diversity increases inter-annual stability in global crop pollinator communities.

While an increasing number of studies indicate that range, diversity and abundance of many wild pollinators has declined, the global area of pollinator-dependent crops has significantly increased over the last few decades. Crop pollination studies to date, have mainly focused on either identifying different guilds pollinating various crops, or on factors driving spatial changes and turnover observed in these communities. The mechanisms driving temporal stability for ecosystem functioning and services, however, remain poorly understood. Our study quantifies temporal variability observed in crop pollinators in 21 different crops across multiple years at a global scale. Using data from 43 studies from six continents, we show that (i) higher pollinator diversity confers greater inter-annual stability in pollinator communities, (ii) temporal variation observed in pollinator abundance is primarily driven by the three most dominant species, and (iii) crops in tropical regions demonstrate higher inter-annual variability in pollinator species richness than crops in temperate regions. We highlight the importance of recognising wild pollinator diversity in agricultural landscapes to stabilize pollinator persistence across years to protect both biodiversity and crop pollination services. Short-term agricultural management practices aimed at dominant species for stabilising pollination services need to be considered alongside longer-term conservation goals focussed on maintaining and facilitating biodiversity to confer ecological stability

Conductivity in nonpolar media: experimental and numerical studies on sodium AOT-hexadecane, lecithin-hexadecane and aluminum(III)-3,5-diisopropyl salicylate-hexadecane systems.

The conductivity behavior of doped hydrocarbon systems is studied by applying impedance spectroscopy. In the case of 3,5-diisopropyl salicylato aluminum (III) the charge carriers are formed by dissociation of the compound and their concentration is proportional to the square root of the solute concentration. In hydrocarbon systems that consist of micelle forming compounds (sodium AOT/ lecithin) a linear dependence of charge carrier concentration on solute concentration is observed in the concentration regime where micelles are present. The conduction mechanisms are studied by numerical solution of a Poisson-Nernst-Planck system that describes the charge transport. We follow two different approaches to extract the degree of micelle dissociation from the impedance data. Firstly, by computing the response of a linear approximation of the Poisson-Nernst-Planck model, and secondly by computing the fully nonlinear response from direct numerical simulations using finite elements. For high and moderate frequencies both approaches agree very well with the experimental data. For small frequencies the response becomes nonlinear and the concept of impedance fails. Furthermore, the numerically computed values for the degree of dissociation are of the same order of magnitude as the values obtained with classical formulas, but still differ by a factor of about 1/3. The direct numerical simulation allows new insight into the conduction mechanisms for different frequency regimes