Related papers: Some aspects on the computational implementation o…
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…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
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…
We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the…
The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed…
An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
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…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
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…
We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary…
We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…
The present paper proposes an inf-sup stable divergence free virtual element method and associated a priori, and a posteriori error analysis to approximate the eigenvalues and eigenfunctions of the Stokes spectral problem in one shot. For…
In this paper we consider the three dimensional exterior Stokes problem and study the solvability of the corresponding continuous and discrete formulations that arise from the coupling of a dual-mixed variational formulation with the…
We propose two globally continuous neural-based variants of the Neural Approximated Virtual Element Method (NAVEM), termed B-NAVEM and P-NAVEM. Both approaches construct local basis functions using pre-trained fully connected neural…
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
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…
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…