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Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved by divergence-free reconstruction operators and results in…

Numerical Analysis · Mathematics 2017-12-06 P. L. Lederer , C. Merdon , J. Schöberl

This paper studies non inf-sup stable finite element approximations to the evolutionary Navier--Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby…

Numerical Analysis · Mathematics 2017-09-27 Javier de Frutos , Bosco García-Archilla , Volker John , Julia Novo

This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative…

Numerical Analysis · Mathematics 2025-10-10 Xiaobing Feng , Liet Vo

We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…

Numerical Analysis · Mathematics 2019-07-10 Dominic Breit , Alan Dodgson

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

In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global…

Numerical Analysis · Mathematics 2022-10-28 Danica Basaric , Maria Lukacova-Medvidova , Hana Mizerova , Bangwei She , Yuhuan Yuan

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…

Numerical Analysis · Mathematics 2020-08-26 Efthymios N. Karatzas , Giovanni Stabile , Leo Nouveau , Guglielmo Scovazzi , Gianluigi Rozza

This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…

Numerical Analysis · Mathematics 2018-06-15 Arbaz Khan , Catherine E. Powell , David J. Silvester

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

We propose an analysis for the stabilized finite element methods proposed in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput., 35(6) 2013,…

Numerical Analysis · Mathematics 2014-06-18 Erik Burman

We explore one-point and two-point statistics of the Navier-Stokes-alpha-beta regularization model at moderate Reynolds number in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier-Stokes-alpha model…

Fluid Dynamics · Physics 2014-08-14 Denis F. Hinz , Tae-Yeon Kim , Eliot Fried

In the present paper, we establish the well-posedness, stability, and (weak) convergence of a fully-discrete approximation of the unsteady $p(\cdot,\cdot)$-Navier-Stokes equations employing an implicit Euler step in time and a discretely…

Numerical Analysis · Mathematics 2024-02-27 Luigi C. Berselli , Alex Kaltenbach

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

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

In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around a…

Analysis of PDEs · Mathematics 2025-02-04 Wasim Akram , Manika Bag , Manil T. Mohan

The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

Numerical Analysis · Mathematics 2020-04-23 Ernesto Cáceres , Johnny Guzmán , Maxim Olshanskii

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

Numerical Analysis · Mathematics 2026-01-27 Gabriel Barrenechea , Cristian Cárcamo , Abner Poza

We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…

Numerical Analysis · Mathematics 2022-10-06 Dominic Breit , Andreas Prohl

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient…

Numerical Analysis · Mathematics 2015-08-27 Eduard Feireisl , Radim Hošek , David Maltese , Antonín Novotný

We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…

Numerical Analysis · Mathematics 2017-08-03 Alejandro Allendes , Enrique Otarola , Richard Rankin