The virtual element method

The present review paper has several objectives. Its primary aim is to give an idea of the general features virtual element methods (VEMs), which were introduced about a decade ago in field numerical for partial differential equations, order allow decompositions computational domain into polygons or polyhedra very shape. Nonetheless, also addressed readers who have already heard (and possibly read) VEMs and are interested gaining more precise information, particular concerning their application specific subfields such as ${C}^1$ -approximations plate bending problems approximations solid fluid mechanics.