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

TL;DR

This paper introduces a new Hybrid High-Order numerical method for the power-law Brinkman problem, capable of handling all flow regimes with robustness and high accuracy across various mesh types and approximation orders.

Contribution

It presents a novel Hybrid High-Order method that is robust across all flow regimes for the power-law Brinkman problem, with comprehensive error analysis and validation.

Findings

Method is robust in all regimes from Stokes to Darcy.

Error estimates account for pre-asymptotic convergence.

Numerical experiments confirm theoretical robustness and accuracy.

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.