Virtual Elements for the Navier-Stokes problem on polygonal meshes

A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the methods are stable and optimally convergent. Several numerical tests are presented, confirming the theoretical predictions. A comparison with some mixed finite elements is also performed

Criar Ciência

Antes de desenvolver o tema ―Criar ciência‖, propriamente dito, sinto a necessidade de definir alguns termos e de enquadrar alguns conceitos. Em primeiro lugar, este capítulo dedica-se às Ciências ditas Exatas e Naturais, sejam elas de caráter fundamental ou aplicado, podendo provavelmente grande parte do que aqui está escrito aplicar-se igualmente à Tecnologia. No entanto, será que os processos e conceitos ligados à criação da Ciência nestas áreas do conhecimento diferem dos que regem as Ciências Humanas e Sociais? Provavelmente não, mas cabe ao leitor responder a esta pergunta através dos textos aqui apresentados. Em segundo lugar, as próprias Ciências ditas Exatas e Naturais abrangem mundos tão diversos e distintos, tanto no que diz respeito às escalas abrangidas (espaciais ou temporais), como ao seu próprio estado de desenvolvimento, pelo que me é obviamente impossível abordar estas ciências no seu conjunto. Com estas palavras exemplifico perfeitamente, o dilema da maior parte dos cientistas: Como falar de um tema sabendo perfeitamente que o que se irá dizer, só se verifica para alguns casos específicos ou até mesmo para uma grande maioria, mas nunca para tudo e todos

A parallel multigrid solver for multi-patch Isogeometric Analysis

Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method, but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-0

A Virtual Element Method for elastic and inelastic problems on polytope meshes

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as a suitable treatment of the displacement gradient. The proposed method allows for general polygonal and polyhedral meshes, it is efficient in terms of number of applications of the constitutive law, and it can make use of any standard black-box constitutive law algorithm. Some theoretical results have been developed for the elastic case. Several numerical results within the 2D setting are presented, and a brief discussion on the extension to large deformation problems is included

An attempt to use color as a tool for high resolution correlations between estuarine sedimentary cores from Algarve (Portugal)

Nowadays, paleoenvironmental and climatological researches focus on studying shortterm climatic changes and one of the more sensitive environments for recording those short-term climatic variations are the high sedimentation rate of coastal regions. Accordingly, 4 estuaries from the Algarve region, south of Portugal, have been cored in order to study sedimentary and climatic variations during recent times (c.a. 5000 yrs). For this purpose, we applied sampling and analytical techniques from deep-sea studies, allowing the acquirement of almost continuous data profiles, as the color data obtained with the spectrophotometer Colortron

Evaluating the performance of GARCH models using White´s Reality Check

time seris, GARCH models, bootstrap, reality check, volatility, financial econometrics, Monte Carlo, forecasting, riskmetrics, moving average

Is it possible to use "twin cores" as a unique sedimentary record? An experimental design based on sediment color

Sedimentary cores are widely used for studying Quaternary records. However, the amount of sediment that is available is proportional to the diameter of the core, which is rarely bigger than 15 cm. One way to obtain more sediment is to use two cores retrieved from almost the same location and use them as if they represent a unique sedimentary record. In the present work, an experimental design has been applied to verify if “twin cores” from an estuary can be considered as representing the same sedimentary record with twice the amount of sediment to study. Because sediment can be characterized based on its color, the variables used as replicates in the experimental design are the three Lab CIE colors acquired with a X-Rite Colortron spectrophotometer. Sediment cores were retrieved from the upper saltmarsh of Gilão River’s estuary, southern Portugal. Twin cores, with in between distances of 50 cm, 100 cm and 200 cm, from two different sites were analysed. Results from a nested ANOVA show that even for the closest twin cores (50 cm apart) there is at least one color variable that shows significant variations between the profiles of both cores. These results clearly show that “twin cores” cannot be used as a unique sedimentary record without any previous testing, at least in such transitional regions

Correlation of estuarine sedimentary cores based on color analysis: an example from the Algarve region (Portugal)

Coastal zones play a significant role in the regional development and have been an important area for human occupation through time. The study of estuarine sediments applied to sea level changes had always been of extreme importance, as it reflects the coastal line evolution, either by local, regional or global changes