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arXiv · 2505.08708

A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible power-law flows

Lourenço Beirão da Veiga·Daniele A. Di Pietro·Kirubell B. Haile
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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.

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Lourenço Beirão da Veiga, Daniele A. Di Pietro, Kirubell B. Haile. 2025-05-13. A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible power-law flows. https://arxiv.org/abs/2505.08708

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