A convergent FV-FEM scheme for the stationary compressible Navier-Stokes equations

07/08/2019
by   Charlotte Perrin, et al.
0

In this paper, we propose a discretization of the multi-dimensional stationary compressible Navier-Stokes equations combining finite element and finite volume techniques. As the mesh size tends to 0, the numerical solutions are shown to converge (up to a subsequence) towards a weak solution of the continuous problem for ideal gas pressure laws p(ρ) = aρ γ , with γ > 3/2 in the three-dimensional case. It is the first convergence result for a numerical method with adiabatic exponents γ less than 3 when the space dimension is three. The present convergence result can be seen as a discrete counterpart of the construction of weak solutions established by P.-L. Lions and by S. Novo, A. Novotný.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/28/2022

Optimal analysis of finite element methods for the stochastic Stokes equations

Numerical analysis for the stochastic Stokes/Navier-Stokes equations is ...
research
01/07/2021

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

First-order convergence in time and space is proved for a fully discrete...
research
03/03/2020

Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations

In this paper, we provide conditions, based solely on the observed data,...
research
06/19/2023

Learning operators for identifying weak solutions to the Navier-Stokes equations

This paper focuses on investigating the learning operators for identifyi...
research
03/24/2020

Advanced Newton Methods for Geodynamical Models of Stokes Flow with Viscoplastic Rheologies

Strain localization and resulting plasticity and failure play an importa...
research
06/23/2021

Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport

We introduce dissipative solutions to the compressible Navier-Stokes sys...

Please sign up or login with your details

Forgot password? Click here to reset