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

2025/09/19 by Marı́a G. Armentano, Armentano, María Gabriela, Mauricio Mendiluce +1
Computer Science · Engineering · #65N15 65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2509.16461

openalex publication_date 2025/09/19 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Citations

• Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains

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