Finite element approximation of the stationary Navier-Stokes problem with non-smooth data
Numerical Analysis
2026-02-09 v2 Numerical Analysis
Abstract
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 system with a regularized boundary solution. Based on the existence of the very weak solution for the Navier-Stokes system with L2 boundary data, and a suitable decomposition of this solution, we obtain a priori error estimates between the approximation of the Navier-Stokes system with non-smooth data and the finite element solution of the associated regularized problem. These estimates allow us to conclude that our approach converges with optimal order.
Cite
@article{arxiv.2509.16461,
title = {Finite element approximation of the stationary Navier-Stokes problem with non-smooth data},
author = {María Gabriela Armentano and Mauricio Mendiluce},
journal= {arXiv preprint arXiv:2509.16461},
year = {2026}
}