Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

The virtual element method is well suited to the formulation of arbitrarily regular Galerkin
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …

We consider the discretization of a boundary value problem for a general linear second-
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …

In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

A family of virtual element methods for the two-dimensional Navier--Stokes equations is
proposed and analyzed. The schemes provide a discrete velocity field which is pointwise …

In the present paper we introduce a Virtual Element Method (VEM) for the approximate
solution of general linear second order elliptic problems in mixed form, allowing for variable …

Abstract Development of models and dedicated numerical methods for dynamics in fractured
rocks is an active research field, with research moving towards increasingly advanced …

In this paper, we address the numerical approximation of linear fourth-order elliptic problems
on polygonal meshes. In particular, we present a novel nonconforming virtual element …

We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with
approximating spaces made of products of low order VEM functions and plane waves. We …

This paper contains two major contributions. First we derive, following the discrete de Rham
(DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes …