The Virtual Element Method with curved edges

In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved interface. While an approximation of the domain with polygons leads, for degree of accuracy $k \geq 2$, to a sub-optimal rate of convergence, we show (both theoretically and numerically) that the proposed curved VEM lead to an optimal rate of convergence

The Differentiation and Promotion of Students’ Rights in Portugal

This investigation includes a differential study (Study 1) and a quasi-experimental research (Study 2). In Study 1, the objective was to establish to what extent students’ rights existed and analyse the differentiation between students’ rights with Portuguese and immigrant mothers, throughout school years. The sample consisted of 537 students with Portuguese and immigrant mothers, distributed by different school years (7th, 9th and 11th grades). The Children’s Rights Scale (Hart et al., 1996; Veiga, 2001) was used. In Study 2, the purpose was to analyse the effects on students’ rights of the use by teachers of a communicational intervention program, supervised by school psychologists. The sample involved 7th and 9th grade students, in a total of four classes, two forming the experimental groups (n = 36) and two the control groups (n = 43); as in Study 1, the Children’s Rights Scale was used. The results indicated the effectiveness of the communicational intervention program on students’ rights and are consistent with previous studies. An implication is that psychologists and teachers, working together and taking a human rights perspective, may develop an important role in projects to promote the students’ rights

Basic principles of hp Virtual Elements on quasiuniform meshes

In the present paper we initiate the study of $hp$ Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size $h$ and in the polynomial degree $p$ in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included

A multidisciplinary approach to study precipitation kinetics and hardening in an Al-4Cu (wt. %) alloy

A multidisciplinary approach is presented to analyse the precipitation process in a model Al-Cu alloy. Although this topic has been extensively studied in the past, most of the investigations are focussed either on transmission electron microscopy or on thermal analysis of the processes. The information obtained from these techniques cannot, however, provide a coherent picture of all the complex transformations that take place during decomposition of supersaturated solid solution. Thermal analysis, high resolution dilatometry, (high resolution) transmission electron microscopy and density functional calculations are combined to study precipitation kinetics, interfacial energies, and the effect of second phase precipitates on the mechanical strength of the alloy. Data on both the coherent and semi-coherent orientations of the {\theta}"/Al interface are reported for the first time. The combination of the different characterization and modelling techniques provides a detailed picture of the precipitation phenomena that take place during aging and of the different contributions to the strength of the alloy. This strategy can be used to analyse and design more complex alloys

Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions