A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

A study of the effect of molecular and aerosol conditions in the atmosphere on air fluorescence measurements at the Pierre Auger Observatory

The air fluorescence detector of the Pierre Auger Observatory is designed to perforin calorimetric measurements of extensive air showers created by Cosmic rays of above 10(18) eV. To correct these measurements for the effects introduced by atmospheric fluctuations, the Observatory contains a group Of monitoring instruments to record atmospheric conditions across the detector site, ail area exceeding 3000 km(2). The atmospheric data are used extensively in the reconstruction of air showers, and are particularly important for the correct determination of shower energies and the depths of shower maxima. This paper contains a summary of the molecular and aerosol conditions measured at the Pierre Auger Observatory since the start of regular operations in 2004, and includes a discussion of the impact of these measurements oil air shower reconstructions. Between 10(18) and 10(20) eV, the systematic Uncertainties due to all atmospheric effects increase from 4% to 8% in measurements of shower energy, and 4 g cm(-2) to 8 g cm(-2) in measurements of the shower maximum. (C) 2010 Elsevier B.V. All rights reserved.