A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows
Numerical Analysis
2025-05-14 v1 Numerical Analysis
Abstract
In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods hinges on a discontinuous Galerkin approximation of the viscous term and a reinforced upwind-type stabilization of the convective term. The derived velocity error estimates account for pre-asymptotic orders of convergence observed in convection-dominated flows through regime-dependent estimates of the error contributions. A complete set of numerical results validate the theoretical findings.
Keywords
Cite
@article{arxiv.2505.08708,
title = {A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible non-Newtonian flows},
author = {Lourenço Beirão da Veiga and Daniele A. Di Pietro and Kirubell B. Haile},
journal= {arXiv preprint arXiv:2505.08708},
year = {2025}
}