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

Daniele A.Di Pietro; Jérôme Droniou; André Harnist

doi:10.1007/s10092-021-00410-z

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

Daniele A.Di Pietro, Jérôme Droniou, André Harnist

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in W¹^,^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.

Original language	English
Article number	19
Number of pages	24
Journal	Calcolo
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s10092-021-00410-z
Publication status	Published - Jun 2021

Keywords

Degenerate Leray–Lions problems
Hybrid High-Order methods
Regime-dependent error estimates

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10.1007/s10092-021-00410-zLicence: CC BY

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abstract = "We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in W1,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.",

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AU - Pietro, Daniele A.Di

AU - Droniou, Jérôme

AU - Harnist, André

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N2 - We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in W1,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.

AB - We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in W1,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.

KW - Degenerate Leray–Lions problems

KW - Hybrid High-Order methods

KW - Regime-dependent error estimates

UR - https://www.scopus.com/pages/publications/85104556423

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DO - 10.1007/s10092-021-00410-z

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JO - Calcolo

JF - Calcolo

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M1 - 19

ER -

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

Abstract

Keywords

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