The virtual element method (VEM) is a generalization of the finite element method (FEM) to meshes composed of general polygons in two dimensions and polyhedra in three dimensions. It is designed to be robust with respect to mesh distortion and geometric singularities, and it can be applied to a wide class of partial differential equations, both linear and nonlinear. VEM is mathematically sound and maintains full compatibility with classical FEMs. Thanks to these features, we hope that VEM can serve as a flexible and effective companion to standard FEM within existing computational codes.
Russo, A. (2026). The Virtual Element Method: Basic Concepts and Recent Engineering Applications. IEEE TRANSACTIONS ON MAGNETICS, 62(7), 1-8 [10.1109/tmag.2026.3656672].
The Virtual Element Method: Basic Concepts and Recent Engineering Applications
Russo, A
2026
Abstract
The virtual element method (VEM) is a generalization of the finite element method (FEM) to meshes composed of general polygons in two dimensions and polyhedra in three dimensions. It is designed to be robust with respect to mesh distortion and geometric singularities, and it can be applied to a wide class of partial differential equations, both linear and nonlinear. VEM is mathematically sound and maintains full compatibility with classical FEMs. Thanks to these features, we hope that VEM can serve as a flexible and effective companion to standard FEM within existing computational codes.
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