Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Immunological parameters in elderly women: Correlations with aerobic power, muscle strength and mood state

Purpose: Our objective was to relate immunological data for healthy but sedentary elderly women to aerobic power, strength, and mood state. Methods: We measured peak aerobic power and one-repetition maximum strength along with mood (depression and fatigue), quality of life and carbohydrate intake on 42 women aged 60-77 years. Standard immunological techniques determined natural killer cell count and cytotoxic activity (NKCA), proliferative responses to phytohemaglutinin and OKT3, various lymphocyte subpopulations (CD3(+), CD3(-)CD19(+), CD56(+), CD4(+), CD8(+), CD56(dim) and CD56(bright)), and markers of activation, maturation, down-regulation and susceptibility to apoptosis (CD25(+), CD28(+), CD45RA(+), CD45RO(+), CD69(+), CD95(+), HLA-DR+). Results: Correlations of immune parameters with aerobic power and strength were very similar for absolute and relative immunological data. In the group as a whole, the only correlation with aerobic power was -0.35 (relative CD4(+)CD69(+) count), but in subjects with values <22.6 mL kg(-1) min(-1) correlations ranged from -0.57 (relative CD4(+)CD45RO(+)) to 0.92 (absolute CD56(dim)HLA-DR+). In terms of muscle strength, univariate correlation coefficients ranged from -0.34 (relative and absolute CD3(+)CD4(+)CD8(+)) to +0.48 (absolute CD3(+)HLA-DR+.) and +0.50 (absolute CD8(+)CD45RA(+)CD45RO(+)). Neither NKCA nor lymphocyte proliferation were correlated with aerobic power or muscle strength. Although mood state and quality of life can sometimes be influenced by an individual's fitness level, our multivariate analyses suggested that depression, fatigue and quality of life were more important determinants of immune profile than our fitness measures. Conclusions: Psychological changes associated with aging may have a substantial adverse effect upon the immune system, and immunological function may be enhanced more by addressing these issues than by focusing upon aerobic or resistance training. (C) 2012 Elsevier Inc. All rights reserved.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

MODEL PARTITIONS AND COMPACT TEST CASE SUITES

We present a generalized test case generation method, called the G method. Although inspired by the W method, the G method, in contrast, allows for test case suite generation even in the absence of characterization sets for the specification models. Instead, the G method relies on knowledge about the index of certain equivalences induced at the implementation models. We show that the W method can be derived from the G method as a particular case. Moreover, we discuss some naturally occurring infinite classes of FSM models over which the G method generates test suites that are exponentially more compact than those produced by the W method.

On reducing test length for FSMs with extra states

A long-standing problem when testing from a deterministic finite state machine is to guarantee full fault coverage even if the faults introduce extra states in the implementations. It is well known that such tests should include the sequences in a traversal set which contains all input sequences of length defined by the number of extra states. This paper suggests the SPY method, which helps reduce the length of tests by distributing sequences of the traversal set and reducing test branching. It is also demonstrated that an additional assumption about the implementation under test relaxes the requirement of the complete traversal set. The results of the experimental comparison of the proposed method with an existing method indicate that the resulting reduction can reach 40%. Experimental results suggest that the additional assumption about the implementation can help in further reducing the test suite length. Copyright (C) 2011 John Wiley & Sons, Ltd.

Perfomance of methods for estimating reference evapotranspiration in the municipalities of Frederico Westphalen and Palmeira das Missoes, State of Rio Grande do Sul, Brazil

The estimation of reference evapotranspiration (ETo), used in water balance, allows to determine soil water content, assisting on irrigation management. The present study aimed to compare simple ETo estimating methods with the Penman-Monteith (FAO), in the folowing time scales: daily, 5, 10, 15 and 30 days and monthly in the counties of Frederico Westphalen and Palmeira das Missoes, in the Rio Grande do Sul state, Brazil. The methods tested had their efficiency improved by increasing the time scale of analysis, keeping the same performance for both locations. The highest and lowest ETo values occurred in December and June, respectively. Most methods underestimated ETo. For any of the time scales Makking and Radiaton FAO24 methods can replace the Penman-Monteith for estimating ETo.