Convergence analysis of a conforming adaptive finite element method for an obstacle problem

The adaptive algorithm for the obstacle problem presented in this paper relies on the jump residual contributions of a standard explicit residual-based a posteriori error estimator. Each cycle of the adaptive loop consists of the steps ‘SOLVE’, ‘ESTIMATE’, ‘MARK’, and ‘REFINE’. The techniques from the unrestricted variational problem are modified for the convergence analysis to overcome the lack of Galerkin orthogonality. We establish R-linear convergence of the part of the energy above its minimal value, if there is appropriate control of the data oscillations. Surprisingly, the adaptive mesh-refinement algorithm is the same as in the unconstrained case of a linear PDE—in fact, there is no modification near the discrete free boundary necessary for R-linear convergence. The arguments are presented for a model obstacle problem with an affine obstacle χ and homogeneous Dirichlet boundary conditions. The proof of the discrete local efficiency is more involved than in the unconstrained case. Numerical results are given to illustrate the performance of the error estimator.     

Possible transformation of YBa2Cu3O7 under pressure

Crystal structure measurements on the high-T _c material YBa₂Cu₃O₇ were carried out under pressure. Several X-ray reflections do not reveal a uniform shift with increasing pressure. Two models are presented, which show the experimental data to be consistent with an extensivec-axis orb-axis decrease, respectively.     

Applications of laser ablation and electrothermal vaporization as sample introduction techniques for ICP-MS

The field of applications of ICP-MS can be further increased by the use of special sample introduction techniques such as laser ablation (LA) and electrothermal vaporization (ETV). In both cases a tandem source for mass spectrometry is formed by the sample introduction device and the ICP. The first source is specifically designed for the volatilization of a sample and it can be used to introduce selectively only certain parts of a sample into the ICP-MS, based either on local distribution (LA) or volatility (ETV). Applications of LA-ICP-MS are the determination of distribution patterns of minor constituents in solid samples such as ceramics, alloys or hard biological structures. Homogeneity testing in the first two types of samples or determination of distribution patterns of trace elements in the latter can be carried out rapidly with high spatial resolution on a multielement basis. The possibility of on-line separation between fractions of different volatility in a sample with ETV-ICP-MS is demonstrated for volcanic eruption products and other samples.