Error analysis for a finite element approximation of the steady p(⋅)-Navier-Stokes equations

2023/11/01 by Luigi C. Berselli, Berselli, Luigi C., Alex Kaltenbach +1 · 1 citation
Engineering · Mathematics · #35J60 #35Q35 #65N15 #65N30 #76A05 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2311.00534

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we examine a finite element approximation of the steady p(⋅)-Navier-Stokes equations (p(⋅) is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Compared to previous results, we treat the convective term and employ a more practicable discretization of the power-law index p(⋅). Numerical experiments confirm the quasi-optimality of the a priori error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure.

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