An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations

In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) An adjoint consistent imposition of the boundary conditions; (ii) An adjoint consistent reformulation of the underlying target functional of practical interest; (iii) Design of appropriate interior-penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L_2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi & Rebay, cf. [11], the standard SIPG method outlined in [25], and an NIPG variant of the new scheme will be undertaken.

Expertise and forms of knowledge in the government of families

This paper examines the relationship between the state and the individual in relation to an aspect of mundane family life – the feeding of babies and young children. The nutritional status of children has long been a matter of national concern and infant feeding is an aspect of family life that has been subjected to substantial state intervention. It exemplifies the imposition upon women the ‘biologico-moral responsibility’ for the welfare of children (Foucault 1991b). The state’s attempts to influence mothers’ feeding practices operate largely through education and persuasion. Through an elaborate state-sponsored apparatus, a strongly medicalised expert discourse is disseminated to mothers. This discourse warns mothers of the risks of certain feeding practices and the benefits of others. It constrains mothers through a series of ‘quiet coercions’ (Foucault 1991c) which seek to render them self-regulating subjects. Using data from a longitudinal interview study, this paper explores how mothers who are made responsible in these medical discourses around child nutrition, engage with, resist and refuse expert advice. It examines, in particular, the rhetorical strategies which mothers use to defend themselves against the charges of maternal irresponsibility that arise when their practices do not conform to expert medical recommendations.