PDF superior TítuloA posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

The rest of the paper is organized as follows. In section 2, we recall the continuous and discrete augmented formulations proposed in [17] for problem (2.1). We develop a residual based a posteriori error analysis and show that the a posteriori error estimator is both reliable and efficient. Then, in section 3, we recall from [18] the augmented varia- tional and discrete schemes proposed in the case of non-homogeneous Dirichlet boundary conditions, and deduce an a posteriori error estimator of residual type which is shown to be both reliable and efficient. Finally, in section 4 we provide several numerical results that illustrate the performance of the augmented Galerkin schemes and confirm the theo- retical properties of the a posteriori error estimators introduced in this paper. Moreover, numerical experiments show that the adaptive algorithms based on these a posteriori error estimators are able to localize the singularities and large stress regions of the solutions.

In Tables 5.5 through 5.10 we provide the individual and total errors, the experimental rates of convergence, the a posteriori error estimators, and the effectivity indices for the uniform and adaptive refinements as applied to Examples 3–5. In this case, uniform refinement means that, given a uniform initial triangulation, each subsequent mesh is obtained from the previous one by dividing each triangle into the four ones arising when connecting the midpoints of its sides. We observe from these tables that the errors of the adaptive procedure decrease much faster than those obtained by the uniform one, which is confirmed by the experimental rates of convergence provided there. This fact can also be seen in Figures 5.1 through 5.3 where we display the total error e (σ, u , γ) vs. the degrees of freedom N for both refinements. As shown by the values of r ( e ), particularly in Example 3 (where r ( e ) approaches 1 / 3 for the uniform refinement), the adaptive method is able to recover, at least approximately, the quasi-optimal rate of convergence O ( h ) for the total error. Furthermore, the effectivity indices remain again bounded from above and below, which confirms the reliability and efficiency of θ for the adaptive algorithm. On the other hand, some intermediate meshes obtained with the adaptive refinement are displayed in Figures 5.4 through 5.6. Note that the method is able to recognize the singularities and the large stress regions of the solutions. In particular, this fact is observed in Example 3 (see Fig. 5.4) where the adapted meshes are highly refined around the singular point (0 , 0). Similarly, the adapted meshes obtained in Examples 4 and 5 (see Figs. 5.5 and 5.6) concentrate the refinements around the interior point (1 / 2 , 1 / 2) and the segment x 1 = 0, respectively, where the largest stresses occur.

In the recent papers [3,16] we analyzed dual-mixed formulations for non-linear boundary value problems in plane elasticity. In the case of incompressible materials, we considered the non-Newtonian model from [5,7], and applied the dual-mixed approach from [11] to study its solvability and finite element approxi- mations. Since the non-linear constitutive law depends on the strain tensor, we introduced this variable and the rotation as further unknowns, which yielded a twofold saddle point operator equation as the resulting variational formulation. Then, we extended the well known PEERS space and defined a stable Galerkin scheme, for which a Bank–Weiser type a posteriori error analysis was also developed.

We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual- mixed approach suitable residual type terms arising from Darcy’s law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple a posteriori error estimator and prove that it is reliable and locally efficient. Finally, we provide several numerical experiments that illustrate the theoretical results and support the use of the corresponding adaptive algorithm in practice.

The rest of the paper is organized as follows. In Section 2 we recall the main features of the augmented dual-mixed method introduced in [11, 13] for the linear elasticity problem with homogeneous Dirichlet boundary con- ditions. Then, we use the Ritz projection of the error to derive the new a posteriori error estimator and show that it is reliable and locally efficient. The extension to the case of non-homogeneous Dirichlet boundary condi- tions is developed in Section 3, where we first recall the dual-mixed method from [12, 13]. Finally, in Section 4 we provide several numerical experiments that illustrate the performance of the corresponding adaptive algorithms and support the theoretical results.

We extend the applicability of the augmented dual-mixed method introduced recently in [4, 5] to the problem of linear elasticity with mixed boundary conditions. The method is based on the Hellinger–Reissner principle and the symmetry of the stress tensor is imposed in a weak sense. The Neuman boundary condition is prescribed in the finite element space. Then, suitable Galerkin least-squares type terms are added in order to obtain an augmented variational formulation which is coercive in the whole space. This allows to use any finite element subspaces to approximate the displacement, the Cauchy stress tensor and the rotation.

Disintegratibility of the films was assessed by means of a disintegration test under lab-scale composting conditions according to the ISO 20200 standard, “Determination of the degree of disintegration of plastic materials under simulated composting conditions in a laboratory-scale test”. For the preparation of solid synthetic waste, 10% of activated mature compost (Vigorhumus H-00, purchased from Burás Profesional, S.A., Girona, Spain) was mixed with 30 wt. % rabbit food, 10 wt. % starch, 5 wt. %. sugar, 1wt. % urea, wt. 4% corn oil and 40wt. % sawdust. The water content of the substrate was around 55 wt. % and the aerobic conditions were guaranteed by gently mixing the compost and periodically adding water according to the standard requirements. The samples were cut from the films (10 x 10 x 0.1 mm 3 ) and buried inside plastic mesh bags to simplify their extraction and allow the contact of the compost with the specimens, and were incubated at 58ºC for 41 days. At different composting times samples were recovered for analysis, washed with distilled water, dried at 40ºC under vacuum for 24 h, and weighed. The degree of disintegration was calculated by normalising the sample weight, at different days of incubation, to the initial weight with Equation (3), where m i is the initial dry mass of the test material and m f is the dry mass of the test

The use of B. bassiana as a mycoinsecticide is promising. From a biological point of view, this fungus can infect many pest insect species, inducing high mortality rates (Uma Devi et al., 2008). From the commercial perspective, spore mass production has been successfully achieved, and there are many companies offering products based on B. bassiana (Seema et al., 2013). Im- provements in the formulation that prolong the shelf life of the product using low cost materials will make mycoinsecticides more competitive, promoting eco-friendly solutions for pest control. This study proposes the use of highly available and low cost volcanic materials as carriers for the formulation of mycoinsecticides using the fungus B. bassiana. Two volcanic ashes and one zeolite mineral were selected, which are amorphous and crystalline aluminosilicates, respectively, and have a common volcanic origin. First, the capacity to enhance the conidial thermotolerance of these materials was evaluated and correlated with their hydric retention properties. From the results obtained, one of these materials was selected to test its capacity to maintain spore viability under different temperature and humidity conditions.

The immunocompromised host: general concepts Pathogenesis and microbiology of infection in patients with… …neutropenia and mucositis …cell-mediated immunodeficiency …with mixed deficits [r]

The foregoing procedure is carried out at the element level, and is strictly local: no crack continuity is enforced or crack exclusion zone defined. This leads in many circumstances to locking after a certain crack growth. Such locking seems to be due to a bad prediction of the cracking direction in the element ahead of the pre-existing crack, as sketched in Fig. 6. To over- come this problem without introducing global algorithms (crack tracking and exclusion zones), a certain amount of crack adaptability within each element is merely introduced. The rationale behind the method is that the estimation of the prin- cipal directions in a triangular element is especially bad at crack initiation due to the high stress gradients in the crack tip zone where the new cracked element is usually located; after the crack grows further, the estimation of the principal stress directions ordinarily improves substantially. Therefore, the crack is allowed to adapt itself to the later variations in the prin- cipal stress direction while its opening is small. This crack adaptation is implemented very easily by stating that while the equivalent crack opening at any particular element is less than a threshold value w e th , the crack direction is recomputed

Therefore, the model to interpolate flight radar tracks in a TMA with the best adjustment is mixed (linear-spline) segmentation in the horizontal plane and linear segmentation in the vertical profile to sim- plify the algorithms. This model will provide average errors between the actual and segmented track of less than 100 m (lateral 34 m, longitudinal 67 m and verti- cal 47 ft) which is appropriated in a terminal area where the minimum standard separation can be 3 nautical miles.

As for non-ionic surfactant – based systems, Triton® X-100 (octyl-phenol ethoxylate) is one of the most used, however, alkyl-phenol ethoxylate surfactants such as this one have a limited biodegradability. Their metabolites of degradation have low solubility and are toxic, for example, nonylphenol has been proven to be an endocrine disrupter (Jobling & Sumpter, 1993). On the other hand, aliphatic fatty alcohol ethoxylates such as PEGDE (penta(ethylene glycol) dodecyl ether) are more environmentally friendly; for nanoparticle synthesis, the technical-grade options are usually chosen due to their lower cost. A special feature of non- ionic surfactant systems is the sensitivity of their hydrophilic-lipophilic properties to temperature, and although sometimes this characteristic is seen as a drawback, the possibility for phase-behavior tuning can be used as an advantage for the formulation of non-ionic microemulsions. In addition, nonionic surfactants have a great capacity of hydration by their ethoxylated (EO) units; hence, an appropriate selection of surfactant, oil and precursor salts/precipitating agent concentration, in combination with the rich structural behavior that such a system may display as a function of temperature, can lead to highly optimized formulations in terms of aqueous phase uptake and hence reactants loading. A good premise to this behavior is the enormous efficiency boost in the formation of middle phase microemulsions by the use of block copolymer surfactants reported by Strey et al. (Jakobs et al., 1999).

This paper studies the numerical approximation of the boundary control for the wave equation in a square domain. It is known that the discrete and semi-discrete models ob- tained by discretizing the wave equation with the usual finite difference or finite element methods do not provide convergent sequences of approximations to the boundary control of the continuous wave equation, as the mesh size goes to zero (see [7, 14]). Here we introduce and analyze a new semi-discrete model based on the space discretization of the wave equa- tion using a mixed finite element method with two different basis functions for the position and velocity. The main theoretical result is a uniform observability inequality which allows us to construct a sequence of approximations converging to the minimal L 2 −norm control

Viral hepatitis has been shown to be associated with various extrahepatic manifestations. These can be seen in both acute and chronic liver disease, may precede or follow overt liver disease. Aims and objects: To study the prevalence of extrahepatic manifestations of viral hepa- titis and follow the course of the disease in response to antiviral therapy whenever indicated. Methods: Pro- spectively 448 patients of viral hepatitis were evaluated for extrahepatic manifestations and patients of glomer- ulonephritis (GN), polyarteritis nodosa (PAN) and cryoglobulinemia were tested for viral markers. All pa- tients were investigated for liver and kidney function tests, hematological workup and viral markers such as HBsAg, HBeAg, Anti HBeAg, HCV RNA, IgM anti HAV and IgM anti HEV. Serum electrophoresis and kidney biopsies were done whenever indicated. In 10 cases of hepatitis B glomerulonephritis immunohis- tochemistry was done on kidney biopsies for demon- stration of hepatitis B surface and core antigen. Results: Of total 448 cases 181 (40.4%) had hepatitis B infection, 142 (31.6%) had hepatitis C infection, 86 (19.1%) hepa- titis E and 39 (8.7%) had hepatitis A infection. Extrahe- patic manifestations were seen in 29 (6.4%) cases and these were cases of GN, PAN, cryoglobulinemia, throm- bocytopenia, agranulocytosis, aplastic anemia and pan- creatitis. Patients with hepatitis A with extrahepatic manifestations showed complete recovery in both hepa- titis and extrahepatic manifestations. Six patients with PAN were treated with interferon of which 4 showed

order reduction. The results against CPU time when integrating till time t = 1 are shown in Figure 3. The time required to calculate the exponential-type matrices has not been considered since those calculations are performed just at the very beginning, and the relative cost of that part would very much depend on the final time of integration. The values of k and h which have been considered are the same as in Figure 1 and, as the error in space is negligible with respect to that in time, the values for the errors are practically the same as in that figure. It is clear that, for each value of k, avoiding order reduction implies a big reduction on the size of the error but a very small increase in computational time. Moreover, although it is not an aim of the paper to recommend any particular method, we have compared the results with the exponential quadrature rule which is based on interpolating F in (11) by a linear polynomial. When integrating (21) with the mentioned rule and the above space discretization, for which L h Q h ≡ 0,

Here q v v ¢  is the Franck – Condon factor, which is given by the square of the overlap integral of the vibrational wave functions of the two electronic states involved in the transition. In this work we have used the Rydberg – Klein – Rees ( RKR ) method to determine the potential energy curves. From these potential energies, the rotationless vibrational wave functions — and hence q v v ¢  — are then obtained by solving the Schrö- dinger equation with the Numerov algorithm.

Although many scientific efforts have been devoted to acknowledging the risks of digital technologies, the question of how computers could be used to improve people’s well-being has been much less explored. This was the main motivation for the development of a novel research area—Positive Technology—which aims at investigating how ICT-based applications and services can be used to foster positive growth of individuals, groups and institutions (Botella et al., 2012; Riva et al., 2012; Gaggioli et al., 2017). This area resulted from the convergence of two main trends. First, the emerging interest in the scientific understanding of conditions and processes that contribute to people happiness and well-being, chiefly represented by the fast-growing movement of Positive Psychology. The second trend was the increasing recognition, in the field of Human-Computer Interaction, of the central importance that human experience, values, and ethical concerns have in the design, development and use of interactive systems. The integration of these two perspectives has led to new questions and possibilities concerning how digital technologies could help shaping positive human functioning, strengths, personal empowerment at the individual level, and of groups and organizations, from a social/interpersonal point of view (Botella et al., 2012).

presents significant differences in optical properties when compared to those of the individual constituents, leading to different impacts on solar radiation levels. This effect is assessed by estimating the direct radiative forcing ( D F) of these aerosols from solar flux models using the radiative parameters derived from the Aerosol Robotic Network (AERONET). These data reveal that, in oceanic and vegetative covers (surface albedo (SA) < 0.30), the aerosol effect at the top of atmosphere (TOA) is always cooling the Earth‐atmosphere system, regardless of the aerosol type. The obtained average values of DF range between −27 ± 15 Wm −2 (aerosol optical depth (AOD) at 0.55 mm, 0.3 ± 0.3) for mineral dust mixed with urban‐industrial aerosols, registered in the East Asia region, and − 34 ± 18 Wm −2 (AOD = 0.8 ± 0.4) for the mixture of the mineral dust and biomass burning particles, observed in the Central Africa region. In the intermediate SA range (0.30 – 0.50) the TOA radiative effect depends on the aerosol absorption properties. Thus, aerosols with single scattering albedo at 0.55 m m lower than ∼ 0.88 lead to a warming of the system, with D F of 10 ± 11 Wm −2 for the mixture of mineral dust and biomass burning. Cases with SA > 0.30 are not present in East Asia region. At the bottom of atmosphere (BOA) the maximum D F values are associated with the highest AOD levels obtained for the mixture of mineral dust and biomass burning aerosols ( − 130 ± 44 Wm − 2 with AOD = 0.8 ± 0.4 for SA < 0.30).

surface deformation, for example), G(x,t) is a temporally peri- odic, spatially inhomogeneous forcing function, F represents nonlinear terms, ∇ 2 = ∂ x 2 + ∂ y 2 is the two-dimensional Lapla- cian operator, and γ is a dimensionless damping parameter. If no spatial dependence or nonlinear effects are considered, then Eq. (2) reduces to Mathieu’s equation (1) for G(t) = 2 + 2f cos(2t). Similar extensions of Mathieu’s equation (1) describing pattern forming systems were studied in Refs. [6–8] for the case of one-dimensional patterns and spatially uniform forcing. Note that, in the absence of damping, forcing and nonlinearity (γ = G = F = 0), Eq. (2) is a wave equation. Traveling wave solutions take the form exp { it + ik · x } with = k = |k|. This simple linear dispersion relation in the undamped unforced case differs from earlier models [6–8] in that the flat solution (k = 0) does not oscillate ( = 0). This feature is consistent with the gravity-capillary surface waves that we are most interested in describing, as is the wavenumber dependence of the damping term. The Zhang-Vi˜nals equations [16], for example, which approximate the Faraday system in the limit of weak damping and large depth, can be linearized to yield a set of damped Mathieu equations describing the evolution of each mode:

Another interesting work regarding estimation in the errors in variables models is described in Cui et.al (2004) [8]. In this paper, the authors assume a linear mixed effects model with measurement error in the variables. The estimators for the fixed parameters, the covariance matrix of random effects and the variance for model error are found by the method of moments. These authors also proved from the theoretical point of view the asymptotic properties of the obtained estimators in their research. They do not discuss the prediction of random effect. The authors assert that the maximum likelihood estimators and the estimators of moments may lose the consistency property if they do not take into account in the model the measurement error.