Related papers: A Virtual Element Method for 2D linear elastic fra…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…
In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time-dependent coupled system of nonlinear partial differential…
Standard Virtual Element Methods (VEM) are based on polynomial projections and require a stabilization term to evaluate the contribution of the non-polynomial component of the discrete space. However, the stabilization term is not uniquely…
The Virtual Element Method (VEM) is a very effective framework to design numerical approximations with high global regularity to the solutions of elliptic partial differential equations. In this paper, we review the construction of such…
We present an hp-adaptive virtual element method (VEM) based on the hypercircle method of Prager and Synge for the approximation of solutions to diffusion problems. We introduce a reliable and efficient a posteriori error estimator, which…
In the present study the software CrackComput, based on the Xfem and Xcrack libraries has been used for three problems- to experiment on the convergence properties of the method applied to elasto-statics crack problems, comparison of stress…
We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use…
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…
Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid…
In this paper, we propose and analyze a mixed virtual element method for the approximation of the eigenvalues and eigenfunctions of the two-dimensional elasticity eigenvalue problem. Under standard assumptions on polygonal meshes, we prove…
We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration…
A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…
Recently, the phase field method has been increasingly used for brittle fractures in soft materials like polymers, elastomers, and biological tissues. When considering finite deformations to account for the highly deformable nature of soft…
In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation…
Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from an explosion in computational cost as the system matrix size…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
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…
This study suggests a fast computational method for crack propagation, which is based on the extended finite element method (X-FEM). It is well known that the X-FEM might be the most popular numerical method for crack propagation. However,…
We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…
Virtual beam diagnostics relies on computationally intensive beam dynamics simulations where high-dimensional charged particle beams evolve through the accelerator. We propose Latent Evolution Model (LEM), a hybrid machine learning…