相关论文: Mesh Quality Agglomeration algorithm for the Virtu…

In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail,…

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…

We study numerically the dispersion and dissipation properties of the plane wave virtual element method and the nonconforming Trefftz virtual element method for the Helmholtz problem. Whereas the former method is based on a conforming…

We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…

We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…

Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…

This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…

Recent advances in the industrial inspection of textured surfaces-in the form of visual inspection-have made such inspections possible for efficient, flexible manufacturing systems. We propose an unsupervised feature memory rearrangement…

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial…

In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…

An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is…

Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE…

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…

We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…

The maximum norm error estimations for virtual element methods are studied. To establish the error estimations, we prove higher local regularity based on delicate analysis of Green's functions and high-order local error estimations for the…