相关论文: H(div) and H(curl)-conforming VEM

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…

In this work, we present a nonhomogeneous version of the classical div-curl type estimates in the setup of elliptic system of complex vector fields with constant coefficients on local Hardy space $h^1$. As an application, we obtain a…

Since its introduction, the Virtual Element Method (VEM) was shown to be able to deal with a large variety of polygons, while achieving good convergence rates. The regularity assumptions proposed in the VEM literature to guarantee 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…

This paper presents the first family of conforming finite element divdiv complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\text{divdiv},\Omega;\mathbb{S})$ are from a current preprint [Chen…

We consider the $C^1$-Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we focus on the discretization of the advective Cahn-Hilliard…

We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…

In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications:…

We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\pmb{H}(\mathrm{curl})$, but not of…

A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…

We present a local construction of H(curl)-conforming piecewise polynomials satisfying a prescribed curl constraint. We start from a piecewise polynomial not contained in the H(curl) space but satisfying a suitable orthogonality property.…

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 generalize the two dimensional mixed finite elements of Arbogast and Correa [T. Arbogast and M. R. Correa, SIAM J. Numer. Anal., 54 (2016), pp. 3332--3356] defined on quadrilaterals to three dimensional cuboidal hexahedra. The…

In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…

We develop a numerical assessment of the Virtual Element Method for the discretization of a diffusion-reaction model problem, for higher "polynomial" order k and three space dimensions. Although the main focus of the present study is to…

We present an hp-adaptive virtual element method (VEM) based on the hypercircle method of Prager and Synge for the approximation of solutions to diffusion problems. We introduce a reliable and efficient a posteriori error estimator, which…

We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an $H^1(\Omega)$-conforming discretization by means of VEM which can make use of general polygonal…

This paper proposes a construction of $C^r$ conforming finite element spaces with arbitrary $r$ in any dimension. It is shown that if $k \ge 2^{d}r+1$ the space $\mathcal P_k$ of polynomials of degree $\le k$ can be taken as the shape…

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element…

We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three…