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The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation…

Numerical Analysis · Mathematics 2021-12-30 Gianmarco Manzini , Annamaria Mazzia

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…

Numerical Analysis · Mathematics 2023-04-25 Erik Burman , Janosch Preuss

We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical…

Numerical Analysis · Mathematics 2022-09-26 Francis R. A. Aznaran , Patrick E. Farrell , Charles W. Monroe , Alexander J. Van-Brunt

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…

Computational Physics · Physics 2025-12-05 Christopher DeGrendele , Nguyen Ly , Francois Cadieux , Michael Barad , Dongwook Lee , Jared Duensing

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

Numerical Analysis · Mathematics 2026-02-10 Lander Besabe , Hyesuk Lee

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

We provide an error analysis for the solution of the nonstationary Stokes problem by a variational method in space and time. We use finite elements of higher order for the approximation in space and a Galerkin-Petrov method with first order…

Numerical Analysis · Mathematics 2025-05-13 Mathias Anselmann , Markus Bause , Gunar Matthies , Friedhelm Schieweck

This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytical tool, our method extends to both convex and non-convex…

Numerical Analysis · Mathematics 2024-08-23 Chunmei Wang

We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…

Numerical Analysis · Mathematics 2025-01-09 Hyun Chul Yoon , S. M. Mallikarjunaiah

Numerical computations of stationary states of fast-rotating Bose-Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method…

Quantum Gases · Physics 2015-05-18 Ionut Danaila , Frederic Hecht

A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…

Numerical Analysis · Mathematics 2019-02-14 Edoardo Artioli , Stefano de Miranda , Carlo Lovadina , Luca Patruno

In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the…

Numerical Analysis · Mathematics 2025-11-05 Arbaz Khan , Felipe Lepe , David Mora , Ricardo Ruíz-Baier , Jesus Vellojin

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 paper studies pressure-robustness for the axisymmetric Stokes problem. The transformation to cylindrical coordinates requires that the radially weighted velocity is divergence-free in the classical sense. Consequently, traditional…

Numerical Analysis · Mathematics 2026-03-16 Philip L. Lederer , Christoph Lehrenfeld , Christian Merdon , Tim van Beeck

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

Numerical Analysis · Mathematics 2017-07-10 Michele Botti , Daniele Di Pietro , Pierre Sochala

The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…

Numerical Analysis · Mathematics 2025-12-19 Lingxiao Li , Haiyan Su , He Zhang , Weiying Zheng

In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…

Numerical Analysis · Mathematics 2023-11-28 Alvin Chen , N. Sukumar

The paper considers grad-div stabilized equal-order finite elements (FE) methods for the linearized Navier-Stokes equations. A block triangular preconditioner for the resulting system of algebraic equations is proposed which is closely…

Numerical Analysis · Mathematics 2024-11-12 Yunhui He , Maxim Olshanskii

We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…

Numerical Analysis · Mathematics 2023-04-04 Daniele Boffi , Ramon Codina , Önder Türk