Related papers: Anisotropic Error Estimates of The Linear Virtual …
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
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…
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 develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably…
In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…
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…
We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed…
The present paper extends the theory of Adaptive Virtual Element Methods (AVEMs) to the three-dimensional meshes showing the possibility to bound the stabilization term by the residual-type error estimator. This new bound enables a…
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…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
We consider the Virtual Element method (VEM) introduced by Beir\~ao da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equations; the method has arbitrary order $k \geq 2$ and…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual 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…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…
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, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt the Hellinger--Reissner variational principle to construct a weak equilibrium…
We propose and analyze an $H^2$-conforming Virtual Element Method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hierarchical construction valid for any dimension $d \ge 2$.…
In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose $C^1$ conforming virtual element method (VEM) of arbitrary order,…