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This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

Numerical Analysis · Mathematics 2025-09-05 Antonio Blanco-Casares , Vishal Kumar , Daniel Mira , Oriol Lehmkuhl

Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…

Numerical Analysis · Mathematics 2014-01-23 Saumya Bajpai , Amiya K. Pani

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated…

Numerical Analysis · Mathematics 2021-04-07 Luca Pegolotti , Martin Pfaller , Alison Marsden , Simone Deparis

The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are…

Numerical Analysis · Mathematics 2016-10-19 Lin Mu , Xiu Ye

We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…

Numerical Analysis · Mathematics 2018-07-24 Erik Burman , Peter Hansbo , Mats G. Larson , Andre Massing , Sara Zahedi

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…

Numerical Analysis · Mathematics 2009-11-11 Kenneth Karlsen , Trygve Karper

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 present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…

Fluid Dynamics · Physics 2026-04-14 Thomas Burton , Sean Symon , Davide Lasagna

We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with $H^1$-conforming pressure…

Numerical Analysis · Mathematics 2019-11-07 John A. Evans , David Kamensky , Yuri Bazilevs

We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…

Numerical Analysis · Mathematics 2024-10-21 Costanza Aricò , Rainer Helmig , Ivan Yotov

In this paper, we propose and develop an optimal nonconforming finite element method for the Stokes equations approximated by the Crouzix-Raviart element for velocity and the continuous linear element for pressure. Previous result in using…

Numerical Analysis · Mathematics 2018-07-10 Jian Li

We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier--Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is…

Numerical Analysis · Mathematics 2021-12-28 Buyang Li , Weifeng Qiu , ZongZe Yang

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…

We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally. In the context of equal-order (piecewise-linear)…

Numerical Analysis · Mathematics 2024-10-10 Hennes Hajduk , Dmitri Kuzmin , Gert Lube , Philipp Öffner

We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…

Numerical Analysis · Mathematics 2023-02-14 Alessia Lucca , Saray Busto , Michael Dumbser

We present a unified variational mechanics framework for cavitating turbulent flows and structural motions via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous…

Fluid Dynamics · Physics 2021-02-22 Suraj R. Kashyap , Rajeev K. Jaiman

In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on…

Numerical Analysis · Mathematics 2020-08-19 Luling Cao , Yinnian He , Jian Li

This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces with elementwise bubble functions, yielding a locally…

Numerical Analysis · Mathematics 2025-11-26 Chun Song , Minfu Feng

Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…

Numerical Analysis · Mathematics 2019-04-12 Philipp W. Schroeder , Christoph Lehrenfeld , Alexander Linke , Gert Lube