Application of the virtual element method for two-dimensions Poisson equations

Resumo

The Virtual Element Method (VEM) emerges to address the need for a wide variety of non-regular polygonal meshes within a computational domain. Widely used in mathematics, physics, and engineering, the Poisson equation — a differential equation that generalizes the Laplace equation — served as one of the initial applications for the development of the Virtual Element Method.This work proposes to evaluate the performance of a two-dimensional VEM applied to the Poisson equation across different mesh types, using linear approximations. The results obtained are compared with those from the Finite Element Method (FEM), serving as a reference. The objective of this work is to assess the accuracy and convergence behavior of the method with various mesh configurations.