A Reynolds-semi-robust H(div)-conforming method for unsteady incompressible power-law flows
arXiv:2505.08708
The paper develops and analyzes an H(div)-conforming discontinuous Galerkin method with upwind stabilization for unsteady incompressible power‑law (non‑Newtonian) flows, providing Reynolds‑semi‑robust and pressure‑robust velocity error estimates and confirming them with numerical experiments.
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.