Pressure and convection robust bounds for continuous interior penalty divergence-free finite element methods for the incompressible Navier-Stokes equations

2023/03/20 by Bosco Garcı́a-Archilla, García-Archilla, Bosco, Julia Novo +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2303.10992

openalex publication_date 2023/03/20 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze a pressure-robust method based on divergence-free mixed finite element methods with continuous interior penalty stabilization. The main goal is to prove an O(h^k+1/2) error estimate for the L² norm of the velocity in the convection dominated regime. This bound is pressure robust (the error bound of the velocity does not depend on the pressure) and also convection robust (the constants in the error bounds are independent of the Reynolds number).

Related

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• Divergence-free Reconstruction Operators for Pressure-Robust Stokes\n Discretizations With Continuous Pressure Finite Elements
• Pressure-robustness in quasi-optimal a priori estimates for the Stokes problem
• Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods
• Guaranteed upper bounds for the velocity error of pressure-robust Stokes\n discretisations