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arXiv · 2509.16461

Finite element approximation of the stationary Navier-Stokes problem with non-smooth data

María Gabriela Armentano·Mauricio Mendiluce
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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.

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María Gabriela Armentano, Mauricio Mendiluce. 2025-09-19. Finite element approximation of the stationary Navier-Stokes problem with non-smooth data. https://arxiv.org/abs/2509.16461

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