Related papers: Virtual element approximation of two-dimensional p…
In this present paper we consider a full divergence-free of high order virtual finite element algorithm to approximate the stationary inductionless magnetohydrodynamic model on polygonal meshes. More precisely, we choice appropriate virtual…
In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green's functions and high-order local error estimations for the…
We introduce the harmonic virtual element method (harmonic VEM), a modification of the virtual element method (VEM) for the approximation of the 2D Laplace equation using polygonal meshes. The main difference between the harmonic VEM and…
In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a…
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail,…
We introduce the Neural Approximated Virtual Element Method, a novel polygonal method that relies on neural networks to eliminate the need for projection and stabilization operators in the Virtual Element Method. In this paper, we discuss…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…
We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…
In this paper, we employ the techniques developed for second order operators to obtain the new estimates of Virtual Element Method for fourth order operators. The analysis is based on elements with proper shape regularity. Estimates for…
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the…
It has been extensively studied in the literature that solving Maxwell equations is very sensitive to the mesh structure, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal…
For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It defines the local projectors and the local degrees of freedom…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…