Related papers: The virtual element method on polygonal pixel-base…
We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we…
In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approximation of problems posed on a curved domain or with a curved…
In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…
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…
This paper introduces a nonconforming virtual element method for general second-order elliptic problems with variable coefficients on domains with curved boundaries and curved internal interfaces. We prove arbitrary order optimal…
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…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$…
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…
We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence in the energy and $L^2$ norms, and validate the theoretical…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element basis functions, thereby eliminating issues concerning…
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
We present a new method to construct Virtual Element spaces on polygons with curved edges.
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 [59] the problem is supposed to have a unique solution, but…
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…