Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part I: A nonlinear scheme

We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which yields an efficient computation with a small number of degrees of freedom. We prove error estimates with the optimal convergence order without any relation between the time increment and the mesh size. The result is valid for both the diffusive and non-diffusive models for the conformation tensor in two space dimensions. We introduce an additional term that yields a suitable structural property and allows us to obtain required energy estimate. The theoretical convergence orders are confirmed by numerical experiments. In a forthcoming paper, Part II, a linear scheme is proposed and the corresponding error estimates are proved in two and three space dimensions for the diffusive model.Comment: See arXiv:1603.01074 for Part II: a linear schem

Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme

This is the second part of our error analysis of the stabilized Lagrange-Galerkin scheme applied to the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear elements, which leads to an efficient computation with a small number of degrees of freedom especially in three space dimensions. In this paper, Part II, we apply a semi-implicit time discretization which yields the linear scheme. We concentrate on the diffusive viscoelastic model, i.e. in the constitutive equation for time evolution of the conformation tensor a diffusive effect is included. Under mild stability conditions we obtain error estimates with the optimal convergence order for the velocity, pressure and conformation tensor in two and three space dimensions. The theoretical convergence orders are confirmed by numerical experiments.Comment: See arXiv:1603.01339 for Part I: a nonlinear schem

Osobnostní rysy dětského delikventa a jejich sociální kořeny

Katedra psychologieFilozofická fakult

Mercosur – porównanie czterech krajów członkowskich na podstawie wybranych wskaźników ekonomicznych

The aim of this paper is to present how countries can be compared on the basis of the development of selected macroeconomic indicators. The economic similarity of the four founding Mercosur countries (i.e., Argentina, Brazil, Paraguay, and Uruguay), based on the development of five selected macroeconomic indicators in the period 1991–2016, is investigated. The following indicators were analyzed: current account balance, GDP per capita, trade-to-GDP ratio, unemployment rate, and the GDP deflator, using data from the World Bank database. Using hierarchical cluster analysis of changes in time series (differences and growth rates), it was found that the obtained clusters of countries are different. For this reason, cluster analysis was carried out for two different groups of indicators on the basis of the averages of the Euclidean distances obtained for the individual indicators.Celem tego artykułu jest ukazanie w jaki sposób można dokonać porównań państw na podstawie wybranych wskaźników makroekonomicznych. Zbadano podobieństwo gospodarek czterech krajów założycielskich Mercosur (tj. Argentyny, Brazylii, Paragwaju i Urugwaju) w analizując zmiany pięciu wybranych wskaźników makroekonomicznych w latach 1991–2016. Przeanalizowano następujące wskaźniki: saldo obrotów bieżących, PKB per capita, wskaźnik handlu do PKB, stopę bezrobocia i deflator PKB, wykorzystując dane z bazy danych Banku Światowego. Za pomocą hierarchicznej analizy skupień zmian szeregów czasowych (różnic i wskaźników wzrostu) wykazano, że uzyskane skupienia poszczególnych krajów są różne. W związku z tym analizę skupień przeprowadzono na podstawie średnich odległości euklidesowych uzyskanych dla poszczególnych wskaźników dla dwóch różnych grup wskaźników

Convergence of a finite volume scheme for the compressible Navier–Stokes system

We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results

Fracture parameters of fly ash geopolymer mortars with carbon black and graphite filler

In this study, the effect of carbon black and graphite filler on the crack initiation and fracture parameters of fly ash geopolymer mortar is investigated. The carbon black was added in the amount of 0.5 and 1.0% and graphite powder in the amount of 5 and 10% relative to the fly ash mass. The reference mixture without any filler was also prepared. The fracture characteristics were determined based on the results of the three-point bending test of prismatic specimens provided with an initial central edge notch. The fracture experiments were conducted at the age of 48 days. The vertical force (F), the displacement measured in the middle of the span length (d), and the crack mouth opening displacement (CMOD) were continuously recorded during the test. The records of fracture tests were subsequently evaluated using the effective crack model, work-of-fracture method, and double-K fracture model. The addition of both fine fillers led to a decrease in monitored mechanical fracture parameters in comparison with reference mortar

Penalization method for the Navier–Stokes–Fourier system

We apply the method of penalization to the Dirichlet problem for the Navier–Stokes–Fourier system governing the motion of a general viscous compressible fluid confined to a bounded Lipschitz domain. The physical domain is embedded into a large cube on which the periodic boundary conditions are imposed. The original boundary conditions are enforced through a singular friction term in the momentum equation and a heat source/sink term in the internal energy balance. The solutions of the penalized problem are shown to converge to the solution of the limit problem. In particular, we extend the available existence theory to domains with rough (Lipschitz) boundary. Numerical experiments are performed to illustrate the efficiency of the method