Virtual element methods

Over the last period, various approaches have been developed to extend finite element methods to non-standard shaped elements (general polygons/polyhedra). The construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis. Very recently, a new evolution of the Mimetic Finite Difference Method has been proposed, taking the name of Virtual Element Method (VEM), see [Beirao da Veiga et al, M3AS,  2013]. The VEM takes the steps from the main ideas of modern mimetic schemes but follows a Galerkin discretization of the problem, and therefore can be fully interpreted as a generalization of the finite element method. The research at MOX  in this context, focuses on both the theoretical/computational approximation properties of the VEM as well as its application to wide class of problems arising in various fields of Engineering

View a list of journal publications and MOX Reports related to VEM.

View a list of theses related to VEM.

Virtual element methods

Second velocity component profile for the lid-driven cavity problem obtained with the VEM on a trapezoidal mesh

Virtual element methods

Streamlines for the lid-driven cavity problem obtained with a the VEM on a trapezoidal mesh