Analysis and implementation of Virtual Element Methods for the Stokes Problem

Stokes equations allow to describe various problems of engineering interest, such as problems of lubrication and sedimentation. A method to solve these types of problem, which allows to obtain a divergence-free solution for the velocity field consistent with the pressure field, is the Virtual Elements Method (VEM). First, the theory of VEM and its application to the Stokes problem were investigated. Subsequently, a tool was developed for the implementation of VEM on Virtual Element spaces of the second order for polygonal meshes, which can deal with geometrically complex polygons, such as non-convex or high aspect ratio elements.