Adaptive space–time finite element solution for Volterra equations arising in viscoelasticity problems

AbstractWe give a short overview of our recent efforts towards constructing adaptive space–time finite element solvers for some partial differential Volterra equations arising in viscoelasticity theory

‘I am not someone who gets skin cancer’: Risk, time and malignant melanoma

‘Delay’ is a term used in the cancer literature since the 1930s to describe the period between self-detection of a concerning sign of possible disease and presentation to a health professional. This linguistic choice carries an implication of blame for apparent failure to manage a risk appropriately, drawing attention away from the contemporaneous perspectives of those who respond to suspicious indicators more or less quickly. We present findings from a grounded theory study of accounts given by 45 patients about their slower or quicker journeys to a diagnosis of cutaneous malignant melanoma, a cancer which can ‘hide in plain sight’. There has been little research exploring in qualitative detail patients’ perspectives on their decision-making about what subsequently turn out to have been signs of this most risky of skin cancers. The findings frame referral time-lapses in terms of normalisation of symptoms, sometimes buttressed by reassurance derived from health promotion messages, disconfirmation of patients’ concerns by their general practitioners and prioritisation of other life concerns. We argue that a shared sense of urgency surrounding melanoma self-referral derives from a clinical representation of current knowledge which conceals numerous evidential uncertainties

Discrete schemes for treating hereditary problems of viscoelasticity and applications

AbstractMathematical models for treating problems of linear viscoelasticity involving hereditary constitutive relations for compressible solids are presented, and their discretisation using finite element methods in space together with quadrature rules in time to treat the hereditary integrals is described. Theoretical error estimates in appropriate Sobolev space settings are given, both as they arise as a result of using a Gronwall inequality, and also from employing a more sensitive comparison theorem which (for the quasistatic problem, and under physically reasonable assumptions on the relaxation function) yields much sharper constants in the estimates.The range of applicability of the mathematical models, and hence the numerical schemes and error estimates are discussed in the context of various materials, primarily polymeric materials, and extensions of the techniques to the modelling of manufacturing processes such as thermoforming are presented