Related papers: Discrete Data Assimilation in the Lorenz and 2D Na…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…
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…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted…
We consider the strong solution of the 2D Navier-Stokes equations in a torus subject to an additive noise. We implement a fully implicit time numerical scheme and a finite element method in space. We prove that the rate of convergence of…
A numerical method for the two-dimensional, incompressible Navier--Stokes equations in vorticity--streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of…
Discrete mechanics is presented as an alternative to the equations of fluid mechanics, in particular to the Navier-Stokes equation. The derivation of the discrete equation of motion is built from the intuitions of Galileo, the principles of…
In this paper, we rigorously derive the compressible one-fluid Navier-Stokes equation from the scaled compressible two-fluid Navier-Stokes-Maxwell equations locally in time under the assumption that the initial data are well prepared. We…
In this article we prove highly improved and flexible Strichartz-type estimates allowing us to generalize the asymptotics we obtained for a stratified and rotating incompressible Navier-Stokes system: for large (and less regular) initial…
In this paper, we introduce a new, fast data assimilation algorithm for a 2D linear advection equation with divergence-free coefficients. We first apply the nodal discontinuous Galerkin (DG) method to discretize the advection equation, and…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are probability measures accounting for spatial correlations, and…
This paper considers a nudging-based scheme for data assimilation for the two-dimensional (2D) Navier-Stokes equations (NSE) with periodic boundary conditions and studies the synchronization of the signal produced by this algorithm with the…
In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…