Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Diageo's 'Stop Out of Control Drinking' campaign in Ireland: an analysis

Background: It has been argued that the alcohol industry uses corporate social responsibility activities to influence policy and undermine public health, and that every opportunity should be taken to scrutinise such activities. This study analyses a controversial Diageo-funded ‘responsible drinking’ campaign (“Stop out of Control Drinking”, or SOOCD) in Ireland. The study aims to identify how the campaign and its advisory board members frame and define (i) alcohol-related harms, and their causes, and (ii) possible solutions. Methods: Documentary analysis of SOOCD campaign material. This includes newspaper articles (n = 9), media interviews (n = 11), Facebook posts (n = 92), and Tweets (n = 340) produced by the campaign and by board members. All material was coded inductively, and a thematic analysis undertaken, with codes aggregated into sub-themes. Results: The SOOCD campaign utilises vague or self-defined concepts of ‘out of control’ and ‘moderate’ drinking, tending to present alcohol problems as behavioural rather than health issues. These are also unquantified with respect to actual drinking levels. It emphasises alcohol-related antisocial behaviour among young people, particularly young women. In discussing solutions to alcohol-related problems, it focuses on public opinion rather than on scientific evidence, and on educational approaches and information provision, misrepresenting these as effective. “Moderate drinking” is presented as a behavioural issue (“negative drinking behaviours”), rather than as a health issue. Conclusions: The ‘Stop Out of Control Drinking’ campaign frames alcohol problems and solutions in ways unfavourable to public health, and closely reflects other Diageo Corporate Social Responsibility (CSR) activity, as well as alcohol and tobacco industry strategies more generally. This framing, and in particular the framing of alcohol harms as a behavioural issue, with the implication that consumption should be guided only by self-defined limits, may not have been recognised by all board members. It suggests a need for awareness-raising efforts among the public, third sector and policymakers about alcohol industry strategies