Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

A boundary value problem approach to too-short arc optical track association

Given a short-arc optical observation with estimated angle-rates, the admissible region is a compact region in the range / range-rate space defined such that all likely and relevant orbits are contained within it. An alternative boundary value problem formulation has recently been proposed where range / range hypotheses are generated with two angle measurements from two tracks as input. In this paper, angle-rate information is reintroduced as a means to eliminate hypotheses by bounding their constants of motion before a more computationally costly Lambert solver or differential correction algorithm is run.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Short-arc tracklet association for geostationary objects

Measurement association and initial orbit determination is a fundamental task when building up a database of space objects. This paper proposes an efficient and robust method to determine the orbit using the available information of two tracklets, i.e. their line-of-sights and their derivatives. The approach works with a boundary-value formulation to represent hypothesized orbital states and uses an optimization scheme to find the best fitting orbits. The method is assessed and compared to an initial-value formulation using a measurement set taken by the Zimmerwald Small Aperture Robotic Telescope of the Astronomical Institute at the University of Bern. False associations of closely spaced objects on similar orbits cannot be completely eliminated due to the short duration of the measurement arcs. However, the presented approach uses the available information optimally and the overall association performance and robustness is very promising. The boundary-value optimization takes only around 2% of computational time when compared to optimization approaches using an initial-value formulation. The full potential of the method in terms of run-time is additionally illustrated by comparing it to other published association methods.

Predictive value of the Acute Low Back Pain Screening Questionnaire and the Örebro Musculoskeletal Pain Screening Questionnaire for persisting problems

A small proportion of individuals with non-specific low back pain (NSLBP) develop persistent problems. Up to 80% of the total costs for NSLBP are owing to chronic NSLBP. Psychosocial factors have been described to be important in the transition from acute to chronic NSLBP. Guidelines recommend the use of the Acute Low Back Pain Screening Questionnaire (ALBPSQ) and the Örebro Musculoskeletal Pain Screening Questionnaire (ÖMPSQ) to identify individuals at risk of developing persistent problems, such as long-term absence of work, persistent restriction in function or persistent pain. These instruments can be used with a cutoff value, where patients with values above the threshold are further assessed with a more comprehensive examination.

Value and pitfalls of neurophysiological monitoring in thoracic and thoracoabdominal aortic replacement and endovascular repair

The aim of our study was to analyze the neurophysiological monitoring method with regard to its potential problems during thoracic and thoracoabdominal aortic open or endovascular repair. Furthermore, preventive strategies to the main pitfalls with this method were developed.

High-resolution computer simulations of stacking of weak bases using a transient pH boundary in capillary electrophoresis. 1. Concept and impact of sample ionic strength

The dynamics of focusing weak bases using a transient pH boundary was examined via high-resolution computer simulation software. Emphasis was placed on the mechanism and impact that the presence of salt, namely, NaCl, has on the ability to focus weak bases. A series of weak bases with mobilities ranging from 5 x 10(-9) to 30 x 10(-9) m2/V x s and pKa values between 3.0 and 7.5 were examined using a combination of 65.6 mM formic acid, pH 2.85, for the separation electrolyte, and 65.6 mM formic acid, pH 8.60, for the sample matrix. Simulation data show that it is possible to focus weak bases with a pKa value similar to that of the separation electrolyte, but it is restricted to weak bases having an electrophoretic mobility of 20 x 10(-9) m2/V x s or quicker. This mobility range can be extended by the addition of NaCl, with 50 mM NaCl allowing stacking of weak bases down to a mobility of 15 x 10(-9) m2/V x s and 100 mM extending the range to 10 x 10(-9) m2/V x s. The addition of NaCl does not adversely influence focusing of more mobile bases, but does prolong the existence of the transient pH boundary. This allows analytes to migrate extensively through the capillary as a single focused band around the transient pH boundary until the boundary is dissipated. This reduces the length of capillary that is available for separation and, in extreme cases, causes multiple analytes to be detected as a single highly efficient peak.

Decision-usefulness of ideal cost- and ideal value accounting for valuation and stewardship

This paper contrasts the decision-usefulness of prototype accounting regimes based on perfect accounting for value, i.e. ideal value accounting (IVA), and perfect matching of cost, i.e. ideal cost accounting (ICA). The regimes are analyzed in the context of a firm with overlapping capacity investments where projects earn excess returns and residual income is utilized as performance indicator. Provided that IVA and ICA systematically differ based on the criterion of unconditional conservatism, we assess their respective decision-usefulness for different valuation- and stewardship-scenarios. Assuming that addressees solely observe current accounting data of the firm, ICA provides information which is useful for valuation and stewardship without reservation whereas IVA entails problems under specific assumptions.

Investigating the value of privacy on online social networks: conjoint analysis

Popularity of Online Social Networks has been recently overshadowed by the privacy problems they pose. Users are getting increasingly vigilant concerning information they disclose and are strongly opposing the use of their information for commercial purposes. Nevertheless, as long as the network is offered to users for free, providers have little choice but to generate revenue through personalized advertising to remain financially viable. Our study empirically investigates the ways out of this deadlock. Using conjoint analysis we find that privacy is indeed important for users. We identify three groups of users with different utility patterns: Unconcerned Socializers, Control-conscious Socializers and Privacy-concerned. Our results provide relevant insights into how network providers can capitalize on different user preferences by specifically addressing the needs of distinct groups in the form of various premium accounts. Overall, our study is the first attempt to assess the value of privacy in monetary terms in this context.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.