Related papers: Virtual element approximation of two-dimensional p…
This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
The use of orthonormal polynomial bases has been found to be efficient in preventing ill-conditioning of the system matrix in the primal formulation of Virtual Element Methods (VEM) for high values of polynomial degree and in presence of…
This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known…
In this work, we develop recent research on the fully mixed virtual element method (mixed-VEM) based on the Banach space for the stationary Boussinesq equation to suggest and analyze a new mixed-VEM for the stationary two-dimensional…
We present two approaches to constructing isoparametric Virtual Element Methods of arbitrary order for linear elliptic partial differential equations on general two-dimensional domains. The first method approximates the variational problem…
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…
In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential problems of the form $\Delta^p u =f$, $p\ge1$. More…
In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element…
The paper deals with the a posteriori error analysis of a virtual element method for the Steklov eigenvalue problem. The virtual element method has the advantage of using general polygonal meshes, which allows implementing very efficiently…
The $H^m$-conforming virtual elements of any degree $k$ on any shape of polytope in $\mathbb R^n$ with $m, n\geq1$ and $k\geq m$ are recursively constructed by gluing conforming virtual elements on faces in a universal way. For the lowest…
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…
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 consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).
In this paper we develop a fully nonconforming virtual element method (VEM) of arbitrary approximation order for the two dimensional Cahn-Hilliard equation. We carry out the error analysis for the semidiscrete (continuous-in-time) scheme…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
In this paper we develop an evolution of the $C^1$ virtual elements of minimal degree for the approximation of the Cahn-Hilliard equation. The proposed method has the advantage of being conforming in $H^2$ and making use of a very simple…
We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…