Virtual Element Method: An overview of formulations

Resumo

The virtual element method has been around for about a decade, and it has been through a lot of development during this period. The method generalizes the finite element method for polytopal elements, while retaining optimal convergence properties. This is achieved mainly by implicitly defined function spaces and the use of polynomial projections. This work presents an overview of the development of the method as formulated for elliptic problems in two and three dimensions, here represented by Poissons equations. The formulations covered are: its original formulation, the modified formulation enabling three-dimensional elements, the Serendipity formulation, and one of the formulations for self-stabilized elements.