Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity

A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity

Stabilized lowest order finite element approximation for linear three-field poroelasticity

A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservation equation we ensure stability and avoid pressure oscillations. Importantly, the discretization leads to a symmetric linear system. For the fully discretized problem we prove existence and uniqueness, an energy estimate and an optimal a-priori error estimate, including an error estimate for the divergence of the fluid flux. Numerical experiments in 2D and 3D illustrate the convergence of the method, show the effectiveness of the method to overcome spurious pressure oscillations, and evaluate the added mass effect of the stabilization term.Comment: 25 page

U.dream goes to market - strategic recommendations for the implementation of u.purpose-s business activities and empirical roadmap for the future

U.Dream is a social enterprise targeted at developing social leadership skills. It recently launched U.Purpose (service) and Crescer com Consciência (product) aiming to ensure future financial sustainability. However, these were launched without conducting a market research and clear guiding strategy. The focus of this project is to assess the attractiveness of the CSR and children’s book markets and U.Dream’s current strategy, providing a strategic revision. As far as U.Purpose is concerned, the analysis highlighted the attractiveness of the market. In Portugal, the CSR consulting market is considerably underdeveloped and is expected to grow on the foreseeable future, which gives U.Dream the opportunity to earn a first mover advantage. Nevertheless, it was underlined that U.Purpose has significant improvements to implement before launching, namely, to develop an extensive marketing strategy and a dedicated U.Purpose team

The Gothic and liminality in three contemporary British novels

Abstract : This dissertation explores how conventional Gothic elements are represented in three contemporary British novels by examining the liminality of spectres, madness, and vampires. Throughout my dissertation, I apply Victor Turner’s theory of liminality to determine how each Gothic symbol named above may be considered liminal. Liminality positions initiates on the margin between two different states of existence: spectres occupy the world between the living and the dead; madness oscillates between sanity and insanity in that lucidity is variable; vampires are caught between the realms of “human” and “monster”. I will evaluate liminality as a theoretical framework that characterises the liminal state forming part of rites of passage; additionally, I will relate this threshold to the Gothic elements including spectres, madness, and vampires that I have identified above. I argue for the resurfacing of the Gothic in the work of Neo-Victorian and twenty-first century British writers’ novels. This analysis is carried out through close readings of Susan Hill’s The Woman in Black (1983), A.N. Wilson’s A Jealous Ghost (2005), and David Mitchell’s Slade House (2015). This close reading examines the ways in which, and to what extent, the texts align with and depart from the Gothic genre in their unique representation of Gothic symbols. My discussion evaluates the spectre in The Woman in Black in relation to the manner in which the novel addresses gender inequality. The novel explores society’s treatment of young unwed mothers during the Victorian era while presenting a plot in which the traditionally gendered roles of victim and villain in the Gothic novel are subverted: instead of the conventional, naïvely represented ‘damsel in distress’, the novel’s victim is a male solicitor while the ‘villain’ is presented as a female spectre. My discussion then moves to A Jealous Ghost, in which the representation of madness is strongly entangled with gender and linked to femininity. Here, the familiar Gothic trope of the protagonist as an unfamiliar, arguably uncanny, character to herself is presented. This aspect of the novel is strengthened in relation to its intertextual references to Henry James’s The Turn of the Screw (1898), and here the female protagonist is characterised as storyteller, victim and villain. I then turn my attention to the vampiric characters presented in David Mitchell’s Slade House, a novel re-evaluating the shortcomings of the present through a postmodern lens while addressing and redressing history and its representations of the vampire figure. Finally, I argue that the texts under study represent the Gothic’s resurfacing in twenty-first century British novels as a means to redress unresolved matters of the past and that their inclusion contributes to our understanding of contemporary Gothic fiction.M.A. (English

Error bounds on block Gauss Seidel solutions of coupled\ud multiphysics problems

Mathematical models in many fields often consist of coupled sub–models, each of which describe a different physical process. For many applications, the quantity of interest from these models may be written as a linear functional of the solution to the governing equations. Mature numerical solution techniques for the individual sub–models often exist. Rather than derive a numerical solution technique for the full coupled model, it is therefore natural to investigate whether these techniques may be used by coupling in a block Gauss–Seidel fashion. In this study, we derive two a posteriori bounds for such linear functionals. These bounds may be used on each Gauss–Seidel iteration to estimate the error in the linear functional computed using the single physics solvers, without actually solving the full, coupled problem. We demonstrate the use of the bound first by using a model problem from linear algebra, and then a linear ordinary differential equation example. We then investigate the effectiveness of the bound using a non–linear coupled fluid–temperature problem. One of the bounds derived is very sharp for most linear functionals considered, allowing us to predict very accurately when to terminate our block Gauss–Seidel iteration.\ud \ud Copyright c 2000 John Wiley & Sons, Ltd

A poroelastic model coupled to a fluid network with applications in lung modelling

Here we develop a lung ventilation model, based a continuum poroelastic representation of lung parenchyma and a 0D airway tree flow model. For the poroelastic approximation we design and implement a lowest order stabilised finite element method. This component is strongly coupled to the 0D airway tree model. The framework is applied to a realistic lung anatomical model derived from computed tomography data and an artificially generated airway tree to model the conducting airway region. Numerical simulations produce physiologically realistic solutions, and demonstrate the effect of airway constriction and reduced tissue elasticity on ventilation, tissue stress and alveolar pressure distribution. The key advantage of the model is the ability to provide insight into the mutual dependence between ventilation and deformation. This is essential when studying lung diseases, such as chronic obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be used to form a better understanding of integrated lung mechanics in both the healthy and diseased states

Trace fossils in the Ecca of northern Natal and their palaeoenviromental significance

Because of the rarity of body fossils in the Ecca Group fossil burrows, tracks and trails are of potential value in supplementing primary sedimentary evidence concerning the palaeoenvironmental factors of bathymetry, energy level and food supply. The three most important ichnogenera are Skolithos, Corophioides and Scolicia. The first two are restricted to the upper portions or Middle Ecca upward-coarsening regressive cycles attributed to delta progradation. They arc representatives of Seilacher's (1967) Skolithos and Glossijungites communities, indicating shallow water conditions with diastems. Scolicia occurs at lower levels in the cycles and corresponds to Seilacher's deeper water Cruziana community. Meandering trails Helminthopsis and Taphrhelminthopsis in the Lower Ecca belong to Seilacher's deep water Nereites community. Less common ichnogenera include the U-burrows Diplocraterion and Rhizocorallium. It has proved impossible positivelv to identify many trace fossils such as short ramifying burrows, chevron trails, dumbbell-shaped surface impressions, digitate tracks and problematic elliptical casts. Trace fossils have not been recognised with certainty in the fluviatile deposits which comprise the bulk or the coal-bearing strata of northern Natal.CSI