# A Hybrid High-Order method for creeping flows of non-Newtonian fluids

@article{Botti2021AHH, title={A Hybrid High-Order method for creeping flows of non-Newtonian fluids}, author={Michele Botti and Daniel Castanon Quiroz and Daniele A. Di Pietro and Andr'e Harnist}, journal={ArXiv}, year={2021}, volume={abs/2003.13467} }

In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for scalar Leray–Lions problems. A complete well-posedness and convergence analysis of the method is carried out…

## 4 Citations

A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour

- MathematicsArXiv
- 2021

This work design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour, and designs and analyzes an HHO scheme based on this weak formulation.

A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes

- Computer ScienceArXiv
- 2022

A novel divergence-preserving velocity reconstruction is introduced that hinges on the solution inside each element of a mixed problem on a subtriangulation, then is used to design discretizations of the body force and convective terms that lead to pressure robustness.

HHO methods for the incompressible Navier-Stokes and the incompressible Euler equations

- Computer ScienceArXiv
- 2021

Two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations are proposed and their robustness with respect to the Reynolds number is investigated and it is found that the resulting numerical scheme is robust up to the inviscid limit, meaning that it can be applied for seeking approximate solutions of the incompressing Euler equations.

Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems

- Mathematics, Computer ScienceCalcolo
- 2021

Novel error estimates are derived for Hybrid High-Order (HHO) discretizations of Leray-Lions problems set in W 1, p with p ∈ (1, 2) by proving that, depending on the degeneracy of the problem, the convergence rate may vary between (k + 1)(p − 1), with k denoting the degree of the HHO approximation.

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