Lourenço Beirão da Veiga is a full professor in numerical analysis at the University of Milano-Bicocca, Italy. His research mainly concerns the development and theoretical analysis of numerical methods for partial differential equations, with a particular focus on solid and fluid mechanics. His more recent interests are on novel and nonstandard methodologies such as isogeometric analysis, mimetic finite differences, and virtual element methods.

Gianmarco Manzini is a research director of the Consiglio Nazionaledelle Ricerche in Pavia, Italy and a senior scientist at the Los Alamos National Laboratory in Los Alamos, New Mexico. His research interests mainly concern the design and implementation of numerical methods for partial differential equations, with a special focus on numerical methods for polygonal and polyhedral meshes such as finite volumes, mimetic finite differences, and virtual element methods.

Provides a comprehensive review of the rapidly expanding field of the virtual element methods

Includes in-depth discussions on the design and analysis of the virtual element method

Covers a vast array of special topics and applications illustrating the wide use of the virtual element method

1 Tommaso Sorgente et al., VEM and the Mesh.- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes.- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions.- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems.- 5 Lourenço Beirão da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics.- 6 Gabriel N. Gatica et al, A virtual marriage à la mode: some recent results on the coupling of VEM and BEM.- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems.- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations.- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation.- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review.- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics.- 12 Sebastián Naranjo Álvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics.- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.