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

@article{Pietro2021ImprovedEE, title={Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems}, author={Daniele A. Di Pietro and J{\'e}r{\^o}me Droniou and Andr'e Harnist}, journal={ArXiv}, year={2021}, volume={abs/2012.05122} }

We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray-Lions problems set in W 1, p with p ∈ (1, 2]. Specifically, we prove that, depending on the degeneracy of the problem, the convergence rate may vary between (k + 1)(p − 1) and (k + 1), with k denoting the degree of the HHO approximation. These regime-dependent error estimates are illustrated by a complete panel of numerical experiments.

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

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2021

The proposed Hybrid High-Order discretization 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 Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type

- Mathematics, Computer ScienceArXiv
- 2021

A Hybrid-High Order (HHO) approximation for a class of quasilinear elliptic problems of nonmonotone type that supports arbitrary order of approximation and general polytopal meshes is designed and analyzed.

## References

SHOWING 1-10 OF 22 REFERENCES

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

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2021

The proposed Hybrid High-Order discretization 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.

Unstabilized Hybrid High-Order method for a class of degenerate convex minimization problems

- MathematicsSIAM J. Numer. Anal.
- 2021

The application of this HHO method to the class of degenerate convex minimization problems allows for a unique $H(\operatorname{div})$ conforming stress approximation $\sigma_h$ and the main results are a~priori and a posteriori error estimates for the stress error $\s Sigma-\sigma-h$ in Lebesgue norms and a computable lower energy bound.

Harnist, A Hybrid High-Order method for creeping flows of non-Newtonian fluids, Submitted

- 2020

The Hybrid High-Order Method for Polytopal Meshes

- Computer Science
- 2020

This monograph provides an introduction to the design and analysis of HHO methods for diffusive problems on general meshes, along with a panel of applications to advanced models in computational mechanics.

A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits

- MathematicsComputer Methods in Applied Mechanics and Engineering
- 2018

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

- Computer ScienceJ. Comput. Phys.
- 2018

A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes

- Mathematics, Computer ScienceMath. Comput.
- 2017

A Hybrid High-Order (HHO) method for steady non-linear Leray–Lions problems is developed and analyzed by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case.

$W^{s,p}$-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray-Lions problems

- Mathematics
- 2016

In this work we prove optimal $W^{s,p}$-approximation estimates (with $p\in[1,+\infty]$) for elliptic projectors on local polynomial spaces. The proof hinges on the classical Dupont--Scott…

Mimetic finite difference approximation of quasilinear elliptic problems

- Mathematics, Computer Science
- 2015

Under a suitable approximation assumption, it is proved that the MFD approximate solution converges, with optimal rate, to the exact solution in a mesh-dependent energy norm.

Approximation of the ?-Stokes equations with equal-order finite elements

- J. Math. Fluid Mech
- 2013