A Hybrid High-Order method for the power-law Brinkman problem with robust error estimates in all regimes

Abstract

In this work we propose and analyze a new Hybrid High-Order method for the Brinkman problem for fluids with power-law viscosity. The proposed method supports general meshes and arbitrary approximation orders and is robust in all regimes, from pure (power-law) Stokes to pure Darcy. Robustness is reflected by error estimates that distinguish the contributions from Stokes- and Darcy-dominated elements as identified by an appropriate dimensionless number, and that additionally account for pre-asymptotic orders of convergence. Theoretical results are illustrated by a complete panel of numerical experiments.