Related papers: A virtual element approximation for the pseudostre…
This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…
In this paper, we propose and analyze a mixed virtual element method for the approximation of the eigenvalues and eigenfunctions of the two-dimensional elasticity eigenvalue problem. Under standard assumptions on polygonal meshes, we prove…
We present a priori and superconvergence error estimates of mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation. In particular, we derive superconvergence estimates for the velocity and a priori…
We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to…
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 propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
In this paper we develop a $C^0$-conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error…
We present and discuss a generalization of the popular MINI mixed finite element for the 2D Stokes equation by means of conforming virtual elements on polygonal meshes. We prove optimal error estimates for both velocity and pressure.…
In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…
In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations for…
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not uniquely determine the velocity-pressure couple. We propose an…
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…
This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…
We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…
In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered…
In this paper, we propose and develop an optimal nonconforming finite element method for the Stokes equations approximated by the Crouzix-Raviart element for velocity and the continuous linear element for pressure. Previous result in using…
This paper is devoted to study the Arnold-Winther mixed finite element method for two dimensional Stokes eigenvalue problems using the stress-velocity formulation. A priori error estimates for the eigenvalue and eigenfunction errors are…
We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for which the…