Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations

We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a piecewise-linear, discontinuous Galerkin method in time combined with a piecewise-linear, conforming finite element method in space. The time mesh is graded appropriately near $t=0$, but the spatial mesh is quasiuniform. Previously, we proved that the error, measured in the spatial $L_2$-norm, is of order $k^{2+\alpha_-}+h^2\ell(k)$, uniformly in $t$, where $k$ is the maximum time step, $h$ is the maximum diameter of the spatial finite elements, $\alpha_-=\min(\alpha,0)\le0$ and $\ell(k)=\max(1,|\log k|)$. Here, we generalize a known result for the classical heat equation (i.e., the case $\alpha=0$) by showing that at each time level $t_n$ the solution is superconvergent with respect to $k$: the error is of order $(k^{3+2\alpha_-}+h^2)\ell(k)$. Moreover, a simple postprocessing step employing Lagrange interpolation yields a superconvergent approximation for any $t$. Numerical experiments indicate that our theoretical error bound is pessimistic if $\alpha<0$. Ignoring logarithmic factors, we observe that the error in the DG solution at $t=t_n$, and after postprocessing at all $t$, is of order $k^{3+\alpha_-}+h^2$.Comment: 24 pages, 2 figure

The Muslim Brotherhood’s Influence and the Democratization of the Middle East

The Muslim Brotherhood is the most well-known and influential Islamist group in the Middle East and has been since its founding in 1928. The group has been condemned by the West, specifically the United States, for being too radical, as well as by other radical Islamist groups, who accuse the Brother hood of embracing democracy and denying jihad. This study aims to determine how the Muslim Brotherhood gained their influence and whether their existence has had a positive or negative effect on democratization in the region. Specifically, it explores how colonialism in the region allowed the Muslim Brotherhood to gain continued political influence, especially following the Arab Spring. To test the hypothesis that the political environment following colonialism in the region was the root cause of the rise of influence of the Muslim Brotherhood, I look at the group’s historical rise in Egypt and Palestine. I then explore the events of the Arab Spring and Intifada and the roles that the group played, both during the uprisings and in their aftermath. Once I have established their level of influence and political positions in and after these movements, I assess whether they have furthered democratization in the region or hurt it. I find that the political environment of remaining colonial elites following the end of colonization in the region is the most likely cause for the group’s increased influence and outsized role in shaping regimes following the Arab Spring. I then assess data collected in Egypt before and then after the Muslim Brotherhood’s candidate, Mohamed Morsi, won the presidency in 2012. Through use of Beetham et. al’s Framework in Assessing the Quality of Democracy: A Practical Guide and survey data from the Arab Barometer, I conclude that, despite their participation in democratic elections, the Muslim Brotherhood ultimately could not be considered to be a positive force for democratization in Egypt, and this has negative implications for its role in the region as a whole

Effective methods for detecting fraudulent financial reporting: practical insights from Big 4 auditors

Purpose Using a qualitative grounded theory approach, this study explores the methods experienced external auditors use to detect fraudulent financial reporting (FFR) during standard audits. Design/methodology/approach Semi-structured interviews were conducted with 24 experienced external auditors to explore the methods they used to detect FFR successfully during standard external audits. Findings The authors find 58 methods used for FFR detection, out of which the following methods are frequently used and help in detecting more than one type of FFR: (1) specific analytical procedures, (2) positive confirmation, (3) understanding of the client's business and industry, (4) the inspection of specific documents, (5) a detailed analysis of the audit client's anti-fraud controls and (6) investigating tip-offs from suppliers, employees and customers. Research limitations/implications Based on the grounded theory approach, the authors theorise that auditors must return to the basics and focus on specific audit procedures highlighted in this study for effective fraud detection. Practical implications The study provides practical guidance, including 58 methods used in audit practice to detect FFR. This knowledge can improve auditors' skills in detecting material misstatements due to fraud. Besides, analytical procedures and positive confirmation helped external auditors in this study detect all forms of FFR, yet they are overlooked in the external audit practice. Therefore, audit firms should emphasise the significance of these audit procedures in their professional audit training programmes. Audit regulators should advise auditors to consider positive confirmation instead of negative confirmation in financial audits to increase the likelihood of FFR detection. Moreover, audit standards (ISA 240 and SAS 99) should explicitly require auditors to conduct a detailed analysis of the client's anti-fraud controls. Originality/value This is the first study to identify actual, effective methods used by external auditors in detecting FFR during the ordinary course of an audit

A Framework for Construction Workspace Management: A Serious Game Engine Approach

Construction workspace is regarded as one of the main constraints on construction sites. Construction workspaces are generally difficult to proactively plan and manage due to the dynamic nature of a site where workspace requirements keep changing as time evolves. However, project managers are looking for ways to develop proactive site plan for the workspaces required for construction activities as this can impact not only on the cost and project duration, but can also contribute to provide a safer site. This research paper presents an approach for integrating workspace management within the planning process using a serious game engine technology. This paper first illustrates a review of the workspace management practices and advanced visualization techniques in the construction industry. Then, it presents a process framework for an interactive decision support system that integrates workspace planning into 5D planning in order to enable safer, efficient and more productive construction sites. The decision support system will identify schedule conflicts, workspace conflicts and the severity of their conflicts, and workspace congestions on a construction site and allow construction planners to resolve spatial conflicts prior to construction. Finally, the paper shows the current progress in the development of an initial prototype and outlines the future work and research. © 2012 American Society of Civil Engineers