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In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r > 2) including both…

We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains. We focus on the case…

Numerical Analysis · Mathematics 2024-08-02 Silvia Bertoluzza , Monica Montardini , Micol Pennacchio , Daniele Prada

In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous…

Numerical Analysis · Mathematics 2018-10-11 Lorenzo Botti , Daniele Di Pietro , Jérôme Droniou

We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=10$). Besides, we discuss possible reasons for which the…

Numerical Analysis · Mathematics 2017-09-14 Lorenzo Mascotto , Franco Dassi

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 design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…

Numerical Analysis · Mathematics 2020-10-16 P. F. Antonietti , G. Manzini , I. Mazzieri , H. Mourad , M. Verani

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 work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations for…

Numerical Analysis · Mathematics 2021-04-12 Sebastian Naranjo-Alvarez , Vrushali Bokil , Vitaliy Gyrya , Gianmarco Manzini

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…

Numerical Analysis · Mathematics 2020-12-03 L. Beirão da Veiga , F. Dassi , C. Lovadina , G. Vacca

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve…

Numerical Analysis · Mathematics 2023-11-01 Zhibao Zheng , Udo Nackenhorst

Generalization of the Chapman-Enskog method to the case of large gradients of hydrodynamic velocity allowed us to obtain an integral (over spatial coordinates) representation of the viscous stress tensor in the Navier-Stokes equation. In…

Fluid Dynamics · Physics 2026-05-14 A. B. Kukushkin

This study presents an extension of the corrected Smagorinsky model, incorporating advanced techniques for error estimation and regularity analysis of far-from-equilibrium turbulent flows. A new formulation that increases the model's…

Fluid Dynamics · Physics 2024-11-11 Rômulo Damasclin Chaves dos Santos

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general…

Numerical Analysis · Mathematics 2018-02-14 L. Beirão da Veiga , F. Brezzi , F. Dassi , L. D. Marini , A. Russo

In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-robustness refers to the fact that, under suitable…

Numerical Analysis · Mathematics 2024-09-12 Daniel Castanon Quiroz , Daniele A. Di Pietro

A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear…

Chaotic Dynamics · Physics 2015-06-26 E. Leveque , F. Toschi , L. Shao , J. -P. Bertoglio

This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an…

Numerical Analysis · Mathematics 2025-07-14 Shuhao Cao , Long Chen , Seulip Lee

This article presents a detailed analysis of the Arrow-Hurwicz iteration applied to the solution of the incompressible Navier-Stokes equations, discretized by a divergence-free mixed virtual element method. Under a set of appropriate…

Numerical Analysis · Mathematics 2025-07-17 Binbin Du , Shenxiang Cheng , Yue Yu , Chuanjun Chen

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

In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…

Numerical Analysis · Mathematics 2023-08-16 Daniel van Huyssteen , Felipe Lopez Rivarola , Guillermo Etse , Paul Steinmann