323 research outputs found
The design of conservative finite element discretisations for the vectorial modified KdV equation
We design a consistent Galerkin scheme for the approximation of the vectorial
modified Korteweg-de Vries equation. We demonstrate that the scheme conserves
energy up to machine precision. In this sense the method is consistent with the
energy balance of the continuous system. This energy balance ensures there is
no numerical dissipation allowing for extremely accurate long time simulations
free from numerical artifacts. Various numerical experiments are shown
demonstrating the asymptotic convergence of the method with respect to the
discretisation parameters. Some simulations are also presented that correctly
capture the unusual interactions between solitons in the vectorial setting
GENDER TRANSITION AS SELF-REALISATION IN LATER LIFE: Interview with a 72 year old Trans woman in Wales
Trans experiences of ageing have, so far, been minimally explored in academic literature; however, older Trans people who have transitioned in later life have much to offer the fields of both Trans Studies and Cultural Gerontology. By drawing on an interview with Jenny-Anne Bishop, a 72-year-old Trans woman, this study suggests that Trans ageing experiences are not adequately accounted for by dominant cultural narratives of ageing, notably decline and age-defying narratives, and instead proposes Laceulle and Baars’ (2014) framework of self-realisation as a suitable alternative. Concurrently, this study serves as an empirical illustration of how self-realisation as a framework for meaning attribution in later life can be applied
Preconditioned Krylov solvers for structure-preserving discretisations
A key consideration in the development of numerical schemes for
time-dependent partial differential equations (PDEs) is the ability to preserve
certain properties of the continuum solution, such as associated conservation
laws or other geometric structures of the solution. There is a long history of
the development and analysis of such structure-preserving discretisation
schemes, including both proofs that standard schemes have structure-preserving
properties and proposals for novel schemes that achieve both high-order
accuracy and exact preservation of certain properties of the continuum
differential equation. When coupled with implicit time-stepping methods, a
major downside to these schemes is that their structure-preserving properties
generally rely on exact solution of the (possibly nonlinear) systems of
equations defining each time-step in the discrete scheme. For small systems,
this is often possible (up to the accuracy of floating-point arithmetic), but
it becomes impractical for the large linear systems that arise when considering
typical discretisation of space-time PDEs. In this paper, we propose a
modification to the standard flexible generalised minimum residual (FGMRES)
iteration that enforces selected constraints on approximate numerical
solutions. We demonstrate its application to both systems of conservation laws
and dissipative systems
The design of conservative finite element discretisations for the vectorial modified KdV equation
We design a consistent Galerkin scheme for the approximation of the vectorial modified Korteweg–de Vries equation with periodic boundary conditions. We demonstrate that the scheme conserves energy up to solver tolerance. In this sense the method is consistent with the energy balance of the continuous system. This energy balance ensures there is no numerical dissipation allowing for extremely accurate long time simulations free from numerical artifacts. Various numerical experiments are shown demonstrating the asymptotic convergence of the method with respect to the discretisation parameters. Some simulations are also presented that correctly capture the unusual interactions between solitons in the vectorial setting
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