Related papers: Robust nonconforming virtual element methods for g…
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…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
We present the essential instruments to deal with Virtual Element Method (VEM) for the resolution of partial differential equations in mixed form. Functional spaces, degrees of freedom, projectors and differential operators are described…
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…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element method (VEM), with the family of polygonal meshes satisfying…
This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known…
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element…
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…
Virtual element methods is a new promising finite element methods using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover…
The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements marked for refinement due to their contribution to the global…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
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…
The Virtual Element Method for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
The purpose of the present paper is to develop $C^1$ Virtual Elements in three dimensions for linear elliptic fourth order problems, motivated by the difficulties that standard conforming Finite Elements encounter in this framework. We…
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…
In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes…