A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems

We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments.

Effect of haptic guidance and error amplification robotic training interventions on the immediate improvement of timing among individuals that had a stroke

Abstract : Many individuals that had a stroke have motor impairments such as timing deficits that hinder their ability to complete daily activities like getting dressed. Robotic rehabilitation is an increasingly popular therapeutic avenue in order to improve motor recovery among this population. Yet, most studies have focused on improving the spatial aspect of movement (e.g. reaching), and not the temporal one (e.g. timing). Hence, the main aim of this study was to compare two types of robotic rehabilitation on the immediate improvement of timing accuracy: haptic guidance (HG), which consists of guiding the person to make the correct movement, and thus decreasing his or her movement errors, and error amplification (EA), which consists of increasing the person’s movement errors. The secondary objective consisted of exploring whether the side of the stroke lesion had an effect on timing accuracy following HG and EA training. Thirty-four persons that had a stroke (average age 67 ± 7 years) participated in a single training session of a timing-based task (simulated pinball-like task), where they had to activate a robot at the correct moment to successfully hit targets that were presented a random on a computer screen. Participants were randomly divided into two groups, receiving either HG or EA. During the same session, a baseline phase and a retention phase were given before and after each training, and these phases were compared in order to evaluate and compare the immediate impact of HG and EA on movement timing accuracy. The results showed that HG helped improve the immediate timing accuracy (p=0.03), but not EA (p=0.45). After comparing both trainings, HG was revealed to be superior to EA at improving timing (p=0.04). Furthermore, a significant correlation was found between the side of stroke lesion and the change in timing accuracy following EA (r[subscript pb]=0.7, p=0.001), but not HG (r[subscript pb]=0.18, p=0.24). In other words, a deterioration in timing accuracy was found for participants with a lesion in the left hemisphere that had trained with EA. On the other hand, for the participants having a right-sided stroke lesion, an improvement in timing accuracy was noted following EA. In sum, it seems that HG helps improve the immediate timing accuracy for individuals that had a stroke. Still, the side of the stroke lesion seems to play a part in the participants’ response to training. This remains to be further explored, in addition to the impact of providing more training sessions in order to assess any long-term benefits of HG or EA.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

La corrección de un error en el análisis financiero con devaluación e inflación

El sesgo antiexportador de nuestras economías, el escaso contacto de nuestros empresarios con el extranjero ha producida efectos perjudiciales para nuestro desarrollo, como también ha generado un total desconocimiento de las finanzas internacionales básicas. Es común observar cómo analistas financieros en nuestro medio confunden conceptos que pueden llevar a decisiones erróneas. Estas confusiones se generan por la escasez de bibliografía actualizada en español; todo viene en inglés y esto ya de por sí es un limitarte.

Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

Análisis de la incidencia de las condiciones de instalación sobre el error de medición de los contadores de agua no-domésticos y su repercusión económica

583 p.

An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

Error analyses reveal contrasting deficits in “theory of mind”: neuropsychological evidence from a 3-option false belief task

Perspective taking is a crucial ability that guides our social interactions. In this study, we show how the specific patterns of errors of brain-damaged patients in perspective taking tasks can help us further understand the factors contributing to perspective taking abilities. Previous work (e.g., Samson, Apperly, Chiavarino, & Humphreys, 2004; Samson, Apperly, Kathirgamanathan, & Humphreys, 2005) distinguished two components of perspective taking: the ability to inhibit our own perspective and the ability to infer someone else’s perspective. We assessed these components using a new nonverbal false belief task which provided different response options to detect three types of response strategies that participants might be using: a complete and spared belief reasoning strategy, a reality-based response selection strategy in which participants respond from their own perspective, and a simplified mentalising strategy in which participants avoid responding from their own perspective but rely on inaccurate cues to infer the other person’s belief. One patient, with a self-perspective inhibition deficit, almost always used the reality-based response strategy; in contrast, the other patient, with a deficit in taking other perspectives, tended to use the simplified mentalising strategy without necessarily transposing her own perspective. We discuss the extent to which the pattern of performance of both patients could relate to their executive function deficit and how it can inform us on the cognitive and neural components involved in belief reasoning.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

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.

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.

Aspectos sociodemográficos y laborales en el error asistencial de enfermería

Objetivo: Valorar cómo influyen las características personales y laborales de los profesionales de enfermería en el error asistencial en hospitalización. Método: Estudio descriptivo transversal realizado en 254 enfermeros de los hospitales públicos de Zaragoza, España. Se administró un cuestionario que contenía preguntas sobre los datos sociodemográficos y laborales del profesional y el error sanitario. Resultados: La muestra estuvo formada predominantemente por mujeres (un 88,6%) con una edad media de 37,4 años. El 45,2% tiene una experiencia profesional menor de 10 años, existiendo un alto índice de movilidad en el puesto de trabajo. Existe una asociación entre la edad, el sexo, la movilidad en el servicio hospitalario y el número de errores cometidos (p<0,05). La sobrecarga laboral y la presión por parte de familiares y pacientes son los factores del entorno laboral que más influyen en el momento de cometer un error asistencial. Conclusiones: Las tasas de error en la práctica enfermera hospitalaria están influenciadas por las características del trabajador y el entorno laboral. Para disminuir su frecuencia habrá que proporcionar a los profesionales la formación adecuada al servicio y prevenir los factores de riesgo modificables como el exceso de cargas de trabajo y la presión del entorno social laboral.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.