Related papers: Adaptive virtual elements based on hybridized, rel…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
We present and analyze a Virtual Element Method (VEM) of arbitrary polynomial order $k\in\mathbb{N}$ for the Laplace-Beltrami equation on a surface in $\mathbb{R}^3$. The method combines the Surface Finite Element Method (SFEM) [Dziuk,…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is…
This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the…
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…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
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 shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
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…
We introduce the Virtual Element Method (VEM) for elliptic eigenvalue problems. The main result of the paper states that VEM provides an optimal order approximation of the eigenmodes. A wide set of numerical tests confirm the theoretical…
The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…
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…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
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 develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing…
A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The…