相关论文: Virtual element approximation of eigenvalue proble…

We propose a lightning Virtual Element Method that eliminates the stabilisation term by actually computing the virtual component of the local VEM basis functions using a lightning approximation. In particular, the lightning VEM approximates…

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 a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…

In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…

In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients. By incorporating…

In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…

The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…

In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region \Omega, within the complex plane. More precisely, we consider three types of regions and their intersections:…

The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Equilibration scales a matrix so that the scaled matrix's row and column norms are equal. Scaling can be…

This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary…

We present a Virtual Element Method (VEM) for the solution of Dirichlet problems for the quasilinear equation $-\text{div} (k(u)\text{grad} u)=f$ with essential boundary conditions. Within the VEM the nonlinear coefficient is evaluated with…

The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation…

We numerically investigate the possibility of defining stabilization-free Virtual Element (VEM) discretizations of advection-diffusion problems in the advection-dominated regime. To this end, we consider a SUPG stabilized formulation of the…

We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…

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…

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…

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…

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…

The virtual element method was introduced 10 years ago and it has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization term of the method…

In this paper we show that approximation can help reduce the space used for self-stabilization. In the classic \emph{state model}, where the nodes of a network communicate by reading the states of their neighbors, an important measure of…