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.