相关论文: Ill-conditioning in the Virtual Element Method: st…

We present two kinds of lowest-order virtual element methods for planar linear elasticity problems. For the first one we use the nonconforming virtual element method with a stabilizing term. It can be interpreted as a modification of the…

The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…

We present in a unified framework new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric…

In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…

This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse…

We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover parameters from given observations where the parameters or the data depend on time. There are…

In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning…

This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…

In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the…

We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference…

We present the design of a mesh quality indicator that can predict the behavior of the Virtual Element Method (VEM) on a given mesh family or finite sequence of polyhedral meshes (dataset). The mesh quality indicator is designed to measure…

In this paper we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is…

A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic…

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 the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we…

This article study the average conditioning for a random underdetermined polynomial system. The expected value of the moments of the condition number are compared to the moments of the condition number of random matrices. An expression for…

In spatial statistics and machine learning, the kernel matrix plays a pivotal role in prediction, classification, and maximum likelihood estimation. A thorough examination reveals that for large sample sizes, the kernel matrix becomes…

Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously…