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This paper establishes strong convergence rates for the spatial finite element discretization of a two-dimensional stochastic Navier--Stokes system with transport noise and no-slip boundary conditions on a convex polygonal domain. The main…

Numerical Analysis · Mathematics 2025-12-15 Binjie Li , Qin Zhou

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…

Numerical Analysis · Mathematics 2013-06-03 Traian Iliescu , Zhu Wang

We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the…

Numerical Analysis · Mathematics 2022-03-23 Dominic Breit , Andreas Prohl

The construction of stable, conservative, and accurate volume dissipation is extended to discretizations that possess a generalized summation-by-parts (SBP) property within a tensor-product framework. The dissipation operators can be…

Numerical Analysis · Mathematics 2026-03-19 Alex Bercik , David A. Craig Penner , David W. Zingg

We study a pointwise tracking optimal control problem for the stationary Navier--Stokes equations; control constraints are also considered. The problem entails the minimization of a cost functional involving point evaluations of the state…

Numerical Analysis · Mathematics 2023-09-27 Francisco Fuica , Enrique Otárola

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration…

Numerical Analysis · Mathematics 2023-08-29 Aaron Brunk , Herbert Egger , Oliver Habrich , Maria Lukacova-Medvidova

We consider error estimates for the fully discretized instationary Navier-Stokes problem. For the spatial approximation we use conforming inf-sup stable finite element methods in conjunction with grad-div and local projection stabilization…

Numerical Analysis · Mathematics 2016-09-06 Daniel Arndt , Helene Dallmann , Gert Lube

The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…

Numerical Analysis · Mathematics 2026-02-09 María Gabriela Armentano , Mauricio Mendiluce

We present two different reduced order strategies for incompressible parameterized Navier-Stokes equations characterized by varying Reynolds numbers. The first strategy deals with low Reynolds number (laminar flow) and is based on a…

Numerical Analysis · Mathematics 2023-08-08 Saddam Hijazi , Shafqat Ali , Giovanni Stabile , Francesco Ballarin , Gianluigi Rozza

The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze

Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…

Fluid Dynamics · Physics 2020-07-13 Rajesh Ranjan , S. Unnikrishnan , Datta Gaitonde

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different…

We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…

Analysis of PDEs · Mathematics 2016-05-24 Ciprian Foias , Cecilia F. Mondaini , Edriss S. Titi

The numerical implementation of finite element discretization method for the stream function formulation of a linearized Navier-Stokes equations is considered. Algorithm 1 is applied using Argyris element. Three global orderings of nodes…

Numerical Analysis · Mathematics 2025-10-20 F. Fairag , N. Almulla

This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the $L^2$ space, which is the critical space for the two-dimensional NS equations to be well-posed. In this…

Numerical Analysis · Mathematics 2025-10-02 Buyang Li , Qiqi Rao , Hui Zhang , Zhi Zhou

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

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the…

Numerical Analysis · Mathematics 2017-07-06 Jean-Claude Latché , Khaled Saleh

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…

Numerical Analysis · Mathematics 2022-01-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

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