Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents

2024/08/28 by Alex Kaltenbach, Kaltenbach, Alex, Julius Jeßberger +1
Computer Science · Engineering · #35J60 #35Q35 #65N12 #65N15 #65N30 #76A05 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2408.15731

openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents p > \tfrac2dd+2. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. A priori error estimates for the velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the a priori error estimate for the velocity vector field. The a priori error estimates for the kinematic pressure are quasi-optimal if p ≤ 2.

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