A Hybrid High-Order Method for the Power-Law Brinkman Problem with Robust Error Estimates in all Regimes
Abstract
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.
Fields of Study & Subjects
Probabilistic and Robust Engineering Design
Matrix Theory and Algorithms
Numerical methods for differential equations
Publication details
- Journal / source
- SIAM Journal on Numerical Analysis
- Volume
- 64
- Issue
- 4
- Pages
- 1764–1793
- Publication date
- 24 August 2026
- Language
- EN