Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen--Cahn/Cahn--Hilliard/Navier--Stokes--Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system

'Real' Nature, 'Aesthetic' Nature and the Making of Artworks: Some Challenges of Cross-Cultural Collaboration

The social and educational benefits of cultural exchange within the realm of art are often asserted. However, what of the meaning and value of the actual artworks arising from those exchanges? This paper analyses the barriers to shared understanding that arose in relation to an extended exchange between Japanese and British artists and philosophers on the connection between Nature and Art, 2011-13. First, cultural interfacing is explored in relation to four types– combinatorial, hierarchic, hermeneutic, and thematic – and the case is made that communalities of practice alone cannot guarantee true cultural integration or understanding. Next, six Japanese and Western concepts of ‘Nature’ – as an ontological entity, a class of objects, a domain, a force, a system and an Ideal - are distinguished in relation to the history and beliefs of those cultures. The argument then moves to the interface between Art and Nature: Nature can be the subject of Art, but can it literally be its content? Finally, the relationship between culture and theory is itself explored in relation to two artworks, and their supposed meanings and links. The Appendices include a detailed summary of the distinctions between Japanese and Western aesthetic systems

Noether type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work we prove a weak Noether type theorem for a class of variational problems which include broken extremals. We then use this result to prove discrete Noether type conservation laws for certain classes of finite element discretisation of a model elliptic problem. In addition we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether's 1st Theorem (E. Noether 1918). We summarise extensive numerical tests, illustrating the conservativity of the discrete Noether law using the $p$--Laplacian as an example.Comment: 17 pages, 3 figures, 3 table