Related papers: The Neural Approximated Virtual Element Method for…
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…
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:…
In this study, we propose a virtual element scheme to solve the Darcy problem in three physical dimensions. The main novelty, here proposed, is that curved elements are naturally handled without any degradation of the solution accuracy. In…
The Virtual Element Method is well suited to the formulation of arbitrarily regular Galerkin approximations of elliptic partial differential equations of order $2p_1$, for any integer $p_1\geq 1$. In fact, the virtual element paradigm…
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 the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we…
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 propose two globally continuous neural-based variants of the Neural Approximated Virtual Element Method (NAVEM), termed B-NAVEM and P-NAVEM. Both approaches construct local basis functions using pre-trained fully connected neural…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
In this paper, we explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the active flux approach \cite{AF1}, which combines the usage of…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive…
In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement…
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model…
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 introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…
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…
Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…
A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise…