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Non divergence-free discretisations for the incompressible Stokes problem may suffer from a lack of pressure-robustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that…

Numerical Analysis · Mathematics 2020-02-06 Derk Frerichs , Christian Merdon

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic…

Numerical Analysis · Mathematics 2018-10-24 Edoardo Artioli , Lourenco Beirão da Veiga , Carlo Lovadina , Elio Sacco

An extension of the restricted Delaunay-refinement algorithm for surface mesh generation is described, where a new point-placement scheme is introduced to improve element quality in the presence of mesh size constraints. Specifically, it is…

Computational Geometry · Computer Science 2016-06-28 Darren Engwirda , David Ivers

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we…

Numerical Analysis · Mathematics 2023-05-15 Franco Brezzi , L. Donatella Marini

We present a simple yet effective method for skeleton-free motion retargeting. Previous methods transfer motion between high-resolution meshes, failing to preserve the inherent local-part motions in the mesh. Addressing this issue, our…

Computer Vision and Pattern Recognition · Computer Science 2023-03-21 Haoyu Wang , Shaoli Huang , Fang Zhao , Chun Yuan , Ying Shan

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…

Numerical Analysis · Mathematics 2023-04-04 Alessandro Russo , N. Sukumar

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…

Numerical Analysis · Mathematics 2021-05-07 Elena Bachini , Gianmarco Manzini , Mario Putti

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…

Numerical Analysis · Mathematics 2020-08-26 Zhen Sun , Malte Braack , Jens Lang

In this work we analyze a virtual element method on polyhedral meshes for solving the sixth-order elliptic problem with simply supported boundary conditions. We apply the Ciarlet-Raviart arguments to introduce an auxiliary unknown…

Numerical Analysis · Mathematics 2022-11-16 Franco Dassi , David Mora , Carlos Reales , Ivàn Velàsquez

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…

Numerical Analysis · Mathematics 2018-10-16 L. Beirão da Veiga , A. Russo , G. Vacca

In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic…

Numerical Analysis · Mathematics 2016-11-29 P. F. Antonietti , G. Manzini , M. Verani

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…

Numerical Analysis · Mathematics 2023-06-07 Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…

Fluid Dynamics · Physics 2025-03-10 Lisong Shi , Chaoxiong Zhang , Chih-Yung Wen

We present a virtual element method for the Reissner-Mindlin plate bending problem which uses shear strain and deflection as discrete variables without the need of any reduction operator. The proposed method is conforming in…

Numerical Analysis · Mathematics 2018-10-23 Lourenço Beirão da Veiga , David Mora , Gonzalo Rivera

This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…

Numerical Analysis · Mathematics 2025-12-29 Yanpeng Gong , Sishuai Li , Fei Qin , Bingbing Xu

We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…

Numerical Analysis · Mathematics 2018-08-28 August Johansson , Benjamin Kehlet , Mats G. Larson , Anders Logg

This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order Virtual Element Method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both…

Numerical Analysis · Mathematics 2019-03-06 D. van Huyssteen , B. D. Reddy

We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and…

Numerical Analysis · Mathematics 2025-03-14 F. Dassi , J. Gedicke , L. Mascotto

In this work we design a novel $C^1$-conforming virtual element method of arbitrary order $k \geq 2$, to solve the biharmonic problem on a domain with curved boundary and internal curved interfaces in two dimensions. By introducing a…

Numerical Analysis · Mathematics 2025-05-30 L. Beirão da Veiga , D. Mora , A. Silgado

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…

Numerical Analysis · Mathematics 2014-03-14 Michael Feischl , Thomas Führer , Dirk Praetorius