Related papers: Convergence Analysis of Virtual Element Methods fo…
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 four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral…
The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…
In this article, we develop the $C^1$-nonconforming $C^0$-conforming virtual element method (VEM) for the vanishing moment approximation of the second-order fully nonlinear Monge-Amp\`ere equation in two dimensions. In the vanishing moment…
The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution $u\in V:=H^2_0(\Omega)$ to the biharmonic equation. The abstract framework allows (even a mixture…
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$). We establish…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…
In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…
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…
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using an independent background discretisation, not aligned with…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in…
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…
We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…
We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
We use the local orthogonal decomposition technique to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale diffusion coefficient. We consider nonsmooth initial data and a backward…