Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Consideration of the relevance of standard quality techniques in Mass Customisation

The business philosophy of Mass Customisation (MC) implies rapid response to customer requests, high efficiency and limited cost overheads of customisation. Furthermore, it also implies the quality benefits of the mass production paradigm are guaranteed. However, traditional quality science in manufacturing is premised on volume production of uniform products rather than of differentiated products associated with MC. This creates quality challenges and raises questions over the suitability of standard quality engineering techniques. From an analysis of relevant MC and quality literature it is argued the aims of MC are aligned with contemporary thinking on quality and that quality concepts provide insights into MC. Quality issues are considered along three dimensions - product development, order fulfilment and customer interaction. The applicability and effectiveness of conventional quality engineering techniques are discussed and a framework is presented which identifies key issues with respect to quality for a spectrum of MC strategies.

Landau-Gutzwiller quasi-particles

We define Landau quasiparticles within the Gutzwiller variational theory and derive their dispersion relation for general multiband Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were based on a phenomenological effective single-particle Hamiltonian. For the one-band Hubbard model we calculate the frst-order corrections in 1/D and find that the corrections to the quasiparticle dispersions are small in three dimensions. They may be largely absorbed in a rescaling of the total bandwidth, unless the system is close to half band filling. Therefore, the Gutzwiller theory in the limit of large dimensions provides quasiparticle bands which are suitable for a comparison with real, three-dimensional Fermi liquids.