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We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…

Numerical Analysis · Mathematics 2023-06-27 Veronica Anaya , Ruben Caraballo , Ricardo Ruiz-Baier , Hector Torres

This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…

Numerical Analysis · Mathematics 2019-02-01 Victor DeCaria , William Layton , Haiyun Zhao

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…

Numerical Analysis · Mathematics 2022-02-02 Jean-Luc Guermond , Martin Kronbichler , Matthias Maier , Bojan Popov , Ignacio Tomas

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…

Numerical Analysis · Mathematics 2022-05-02 Jad Doghman

This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…

Numerical Analysis · Mathematics 2018-03-20 Philipp W. Schroeder , Gert Lube

In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and…

Numerical Analysis · Mathematics 2022-03-15 Di Yang , Yinnian He

We introduce a surface finite element method for the numerical solution of Navier-Stokes equations on evolving surfaces with a prescribed deformation of the surface in normal direction. The method is based on approaches for the full surface…

Numerical Analysis · Mathematics 2023-06-16 Veit Krause , Eric Kunze , Axel Voigt

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

This paper studies inf-sup stable finite element discretizations of the evolutionary Navier--Stokes equations with a grad-div type stabilization. The analysis covers both the case in which the solution is assumed to be smooth and…

Numerical Analysis · Mathematics 2017-05-29 Javier de Frutos , Bosco García-Archilla , Volker John , Julia Novo

Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…

Numerical Analysis · Mathematics 2019-10-29 Naveed Ahmed , Gunar Matthies

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…

Analysis of PDEs · Mathematics 2015-06-19 Hakima Bessaih , Eric Olson , E. S. Titi

This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…

Analysis of PDEs · Mathematics 2024-01-05 Piotr Krzyżanowski , Sadokat Malikova , Piotr B. Mucha , Tomasz Piasecki

The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…

Fluid Dynamics · Physics 2007-05-23 Georgy Burde , Alexander Zhalij

This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Monica Nonino , Francesco Ballarin , Gianluigi Rozza

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Michael Wolfgang Kaiser , Thomas-Peter Fries

We investigate theoretically and numerically the use of the Least-Squares Finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based…

Fluid Dynamics · Physics 2020-04-20 Alexander Schwarz , Richard Dwight

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

We consider the steady Navier-Stokes system with mixed boundary conditions, in subdomains of a holdall domain. We study, via the penalization method, its approximation properties. Error estimates, obtained using the extension operator,…

Optimization and Control · Mathematics 2025-08-29 Cornel Marius Murea , Dan Tiba

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

Analysis of PDEs · Mathematics 2016-07-15 Šimon Axmann , Piotr B. Mucha , Milan Pokorný

We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen