Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

The transition movement and food sovereignty: from local resilience to global engagement in food system transformation

The emergence of grassroots social movements variously preoccupied with a range of external threats, such as diminishing supplies of fossil energy or climate change, has led to increased interest in the production of local food. Drawing upon the notion of cognitive praxis, this article utilises transition as a trajectory guided by an overarching cosmology that brings together a broad social movement seeking a more resilient future. This ‘grand narrative’ is reinforced by ‘transition movement intellectuals’ who serve to shape an agenda of local preparedness in the face of uncertainty, rather than structural analysis of the global system. In this context, growing and producing food offers important multi-functional synergies by reconnecting people to place and its ecological endowments and serves to provide a vital element in civic mobilisation. Yet, local food could also become a means to build international solidarity in defence of food sovereignty and establish a global coalition opposed to the corporate agri-food agenda of biotechnologies, land grabbing and nutritional impoverishment.

Specification of optimum holistic building environmental and energy performance information to support informed decision making

Political drivers such as the Kyoto protocol, the EU Energy Performance of Buildings Directive and the Energy end use and Services Directive have been implemented in response to an identified need for a reduction in human related CO2 emissions. Buildings account for a significant portion of global CO2 emissions, approximately 25-30%, and it is widely acknowledged by industry and research organisations that they operate inefficiently. In parallel, unsatisfactory indoor environmental conditions have proven to negatively impact occupant productivity. Legislative drivers and client education are seen as the key motivating factors for an improvement in the holistic environmental and energy performance of a building. A symbiotic relationship exists between building indoor environmental conditions and building energy consumption. However traditional Building Management Systems and Energy Management Systems treat these separately. Conventional performance analysis compares building energy consumption with a previously recorded value or with the consumption of a similar building and does not recognise the fact that all buildings are unique. Therefore what is required is a new framework which incorporates performance comparison against a theoretical building specific ideal benchmark. Traditionally Energy Managers, who work at the operational level of organisations with respect to building performance, do not have access to ideal performance benchmark information and as a result cannot optimally operate buildings. This thesis systematically defines Holistic Environmental and Energy Management and specifies the Scenario Modelling Technique which in turn uses an ideal performance benchmark. The holistic technique uses quantified expressions of building performance and by doing so enables the profiled Energy Manager to visualise his actions and the downstream consequences of his actions in the context of overall building operation. The Ideal Building Framework facilitates the use of this technique by acting as a Building Life Cycle (BLC) data repository through which ideal building performance benchmarks are systematically structured and stored in parallel with actual performance data. The Ideal Building Framework utilises transformed data in the form of the Ideal Set of Performance Objectives and Metrics which are capable of defining the performance of any building at any stage of the BLC. It is proposed that the union of Scenario Models for an individual building would result in a building specific Combination of Performance Metrics which would in turn be stored in the BLC data repository. The Ideal Data Set underpins the Ideal Set of Performance Objectives and Metrics and is the set of measurements required to monitor the performance of the Ideal Building. A Model View describes the unique building specific data relevant to a particular project stakeholder. The energy management data and information exchange requirements that underlie a Model View implementation are detailed and incorporate traditional and proposed energy management. This thesis also specifies the Model View Methodology which complements the Ideal Building Framework. The developed Model View and Rule Set methodology process utilises stakeholder specific rule sets to define stakeholder pertinent environmental and energy performance data. This generic process further enables each stakeholder to define the resolution of data desired. For example, basic, intermediate or detailed. The Model View methodology is applicable for all project stakeholders, each requiring its own customised rule set. Two rule sets are defined in detail, the Energy Manager rule set and the LEED Accreditor rule set. This particular measurement generation process accompanied by defined View would filter and expedite data access for all stakeholders involved in building performance. Information presentation is critical for effective use of the data provided by the Ideal Building Framework and the Energy Management View definition. The specifications for a customised Information Delivery Tool account for the established profile of Energy Managers and best practice user interface design. Components of the developed tool could also be used by Facility Managers working at the tactical and strategic levels of organisations. Informed decision making is made possible through specified decision assistance processes which incorporate the Scenario Modelling and Benchmarking techniques, the Ideal Building Framework, the Energy Manager Model View, the Information Delivery Tool and the established profile of Energy Managers. The Model View and Rule Set Methodology is effectively demonstrated on an appropriate mixed use existing ‘green’ building, the Environmental Research Institute at University College Cork, using the Energy Management and LEED rule sets. Informed Decision Making is also demonstrated using a prototype scenario for the demonstration building.

Engineering of metal oxide interfaces for renewable energy applications

Diminishing non-renewable energy resources and planet-wide de-pollution on our planet are among the major problems which mankind faces into the future. To solve these problems, renewable energy sources such as readily available and inexhaustible sunlight will have to be used. There are however no readily available photocatalysts that are photocatalytically active under visible light; it is well established that the band gap of the prototypical photocatalyst, titanium dioxide, is the UV region with the consequence that only 4% of sun light is utilized. For this reason, this PhD project focused on developing new materials, based on titanium dioxide, which can be used in visible light activated photocatalytic hydrogen production and destruction of pollutant molecules. The main goal of this project is to use simulations based on first principles to engineer and understand rationally, materials based on modifying TiO2 that will have the following properties: (1) a suitable band gap in order to increase the efficiency of visible light absorption, with a gap around 2 – 2.5 eV considered optimum. (2). The second key aspect in the photocatalytic process is electron and hole separation after photoexcitation, which enable oxidation/reduction reactions necessary to i.e. decompose pollutants. (3) Enhanced activity over unmodified TiO2. In this thesis I present results on new materials based on modifying TiO2 with supported metal oxide nanoclusters, from two classes, namely: transition metal oxides (Ti, Ni, Cu) and p-block metal oxides (Sn, Pb, Bi). We find that the deposited metal oxide nanoclusters are stable at rutile and anatase TiO2 surfaces and present an analysis of changes to the band gap of TiO2, identifying those modifiers that can change the band gap to the desirable range and the origin of this. A successful collaboration with experimental researchers in Japan confirms many of the simulation results where the origin of improved visible light photocatalytic activity of oxide nanocluster-modified TiO2 is now well understood. The work presented in this thesis, creates a road map for the design of materials with desired photocatalytic properties and contributes to better understanding these properties which are of great application in renewable energy utilization.