Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in Antonietti et al. [Math. Model. Numer. Anal., 41(1):21-54, 2007] and [Math. Model. Numer. Anal., submitted, 2006] to the (non-consistent) super penalty discontinuos Galerkin methods introduced by Babuska et al. [SIAM J. Numer. Anal., 10:863-875, 1973] and by Brezzi et al. [Numer. Methods Partial Differential Equations, 16(4):365-378, 2000]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments demonstrating the theoretical results.

Established corticosteroid creams should be applied only once daily in patients with atopic eczema

Atopic eczema affects many adults and up to 20% of children,1 with health costs comparable to diabetes2 and asthma.3 One community survey of 1760 young children in the United Kingdom found that 84% had mild eczema, 14% moderate, and 2% severe eczema.4 Topical corticosteroids are a mainstay of treatment for inflammatory episodes.5 Most long established topical corticosteroids such as betamethasone valerate or hydrocortisone are applied at least twice daily, but three newer preparations (mometasone, fluticasone, and methylprednisolone) have been developed for once daily application. Here, I propose that established preparations need be applied only once daily.