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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…

Numerical Analysis · Mathematics 2023-12-19 H. Wells , M. E. Hubbard , A. Cangiani

In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…

Numerical Analysis · Mathematics 2022-06-01 N. Sukumar , Michael R. Tupek

The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…

Numerical Analysis · Mathematics 2024-03-26 Antônio Tadeu Azevedo Gomes , Weslley da Silva Pereira , Frédéric Valentin

In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…

Computational Engineering, Finance, and Science · Computer Science 2021-10-05 Marco Lo Cascio

We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the…

Numerical Analysis · Mathematics 2023-10-16 Andrea Borio , Carlo Lovadina , Francesca Marcon , Michele Visinoni

Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…

Numerical Analysis · Mathematics 2026-02-17 Eric T. Chung , Hyea Hyun Kim , Xiang Zhong

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Jacopo Bonari , Maria R. Marulli , Nora Hagmeyer , Matthias Mayr , Alexander Popp , Marco Paggi

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt the Hellinger--Reissner variational principle to construct a weak equilibrium…

Numerical Analysis · Mathematics 2024-02-29 Alvin Chen , Joseph E. Bishop , N. Sukumar

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…

Numerical Analysis · Mathematics 2019-09-15 Lourenco Beirão da Veiga , Franco Dassi , Alessandro Russo

The material point method (MPM) is frequently used to simulate large deformations of nearly incompressible materials such as water, rubber, and undrained porous media. However, MPM solutions to nearly incompressible materials are…

Numerical Analysis · Mathematics 2024-10-29 Yidong Zhao , Chenfanfu Jiang , Jinhyun Choo

Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…

Numerical Analysis · Mathematics 2026-05-21 Paulo Akira F. Enabe , Rodrigo Provasi

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Benjamin Marussig , Thomas Rüberg , Jürgen Zechner , Lars Kielhorn , Thomas-Peter Fries

In this paper we analyze a virtual element method (VEM) for a pseudostress formulation of the Stokes eigenvalue problem. This formulation allows to eliminate the velocity and the pressure, leading to an elliptic formulation where the only…

Numerical Analysis · Mathematics 2021-04-07 Felipe Lepe , Gonzalo Rivera

We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).

Numerical Analysis · Mathematics 2017-10-03 Susanne C. Brenner , Li-yeng Sung

This paper proposes a virtual element method (VEM) combined with a second-order implicit-explicit scheme based on the scalar auxiliary variable (SAV) method for the incompressible magnetohydrodynamics (MHD) equations. We employ the BDF2…

Numerical Analysis · Mathematics 2024-10-25 Xiaojing Dong , Yunqing Huang , Tianwen Wang

In this paper we introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…

Numerical Analysis · Mathematics 2026-01-29 Felipe Lepe , Gonzalo Rivera

We present an a posteriori error analysis for the mixed virtual element method (mixed VEM) applied to second order elliptic equations in divergence form with mixed boundary conditions. The resulting error estimator is of residual-type. It…

Numerical Analysis · Mathematics 2019-04-24 Andrea Cangiani , Mauricio Munar

We introduce a new Eulerian simulation framework for liquid animation that leverages both finite element and finite volume methods. In contrast to previous methods where the whole simulation domain is discretized either using the finite…

Graphics · Computer Science 2023-01-18 Tatsuya Koike , Shigeo Morishima , Ryoichi Ando

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…

Analysis of PDEs · Mathematics 2017-03-14 M. Campo , J. R. Fernández , Á. Rodríguez-Arós , J. M. Rodríguez

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…

Numerical Analysis · Mathematics 2022-08-23 Tommaso Sorgente , Fabio Vicini , Stefano Berrone , Silvia Biasotti , Gianmarco Manzini , Michela Spagnuolo