The present review paper has several objectives. Its primary aim is to give an idea of the
general features of virtual element methods (VEMs), which were introduced about a decade …

We present the design of a mesh quality indicator that can predict the behavior of the Virtual
Element Method (VEM) on a given mesh family or a finite sequence of polyhedral meshes …

In the present paper we initiate the challenging task of building a mathematically sound
theory for adaptive virtual element methods (AVEMs). Among the realm of polygonal …

We discuss the p-and h p-versions of the virtual element method for the approximation of
eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of …

The virtual element method is an extension of the finite element method permitting arbitrary
polygonal/polyhedral element geometry. The method's mesh flexibility is well-known and is …

We design the conforming virtual element method for the numerical approximation of the two‐
dimensional elastodynamics problem. We prove stability and convergence of the …

In the discretization of differential problems on complex geometrical domains, discretization
methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh …

In this paper, we propose a conforming virtual element method for the Helmholtz
transmission eigenvalue problem of anisotropic media. By using 𝕋-coercivity theory, the …

In this paper a posteriori error analysis of virtual element method (VEM) for the optimal
control problem governed by general elliptic equation is presented. The virtual element …

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very
complex geometries. In the present paper we discuss the use of polygonal mesh refinement …