Virtual Element Method for 3D Poisson Equation

Resumo

This work reports some of the challenges met with when implementing the Virtual Element Method
(VEM) for Poisson’s problem in a three-dimensional setting. The method’s generalization of the Finite Element
Method (FEM) for polytopal shapes and arbitrary order introduces many challenges, such as integration over the
element, mesh generation, etc. There is a significant increase in complexity when going from a two-dimensional
to a three-dimensional implementation of the method, thus the main topic of this work. The Poisson problem is
chosen because of its simplicity, allowing the focus to remain on the method itself. The main comparisons are
between the two and three-dimensional versions of the method, as well as between the latter and the equivalent
Finite Element Method.