Recent developments in Virtual Elements at the University of Milano - Bicocca
The present page represents the research on the Virtual Element Method developed by the team at the Department of Mathematics and Applications (University of Milano-Bicocca), since the start up date of the ERC CoG project CAVE (year 2016), that is strongly supporting our work in this field.
Nowadays the VEM method has developed a lot worldwide, therefore our results are only a small part of what can be found around.
The Virtual Element Method (VEM, born in 2013) is a novel technology for the discretization of partial differential equations (PDEs), that shares the same variational background as the Finite Element Method.
First but not only, the VEM responds to the strongly increasing interest in using general polyhedral and polygonal meshes in the approximation of PDEs without the limit of using tetrahedral or hexahedral grids.
By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrixes, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity.
For instance, the VEM easily allows for polygonal/polyhedral meshes (even nonconforming) with non-convex elements and possibly with curved faces; it allows for discrete spaces of arbitrary C^k regularity on unstructured meshes.
A start-up package on Virtual Elements can be found in the following link.
It includes a pair of initial papers (the first seminal one and the one related to the coding of the scheme), and also the slides of the course on Virtual Elements held in June 2018 at the Dobbiaco Summer School. It also includes a MATLAB code for a simple model problem, but that can be used a starting point for further developments by any researcher.
People interested in the subject can also contact one person of the group for further information.
