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

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

Questions to Assist in Designing Supplementary Materials

Have you ever walked into an elementary classroom and thought you were in the Christmas display window of F.A.O. Schwartz toy store? The teacher is, putting it mildly, creative and talented at making materials. Many of us are not this gifted, yet want to generate supplementary materials of the teacher-made variety for our own students. This is a good reason for becoming involved in designing and producing materials. A secon and even more practical reason is to help solve a real problem: the classroom is deficient in materials and there is little or no financial support available. What would you do in a similar situation