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2020 | OriginalPaper | Chapter

Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes

Author : J. Droniou

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Publisher: Springer International Publishing

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Abstract

We explore the effects of mesh skewness on the accuracy of standard Hybrid High-Order (HHO) schemes for anisotropic diffusion equations. After defining a notion of regular skewed mesh sequences, which allows, e.g., for elements that become more and more elongated during mesh refinement, we establish an error estimate in which we precisely track the dependency of the local multiplicative constants in terms of the diffusion tensor and mesh skewness. This dependency makes explicit an interplay between the local diffusion properties and the distortion of the elements. We then provide several numerical results to assess the practical convergence properties of HHO for highly anisotropic diffusion or highly distorted meshes. These tests indicate a more robust behaviour than the theoretical estimate predicts.

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next chapter -Convergence of Finite Volume Solutions of the Euler Equations
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Metadata
Title
Interplay Between Diffusion Anisotropy and Mesh Skewness in Hybrid High-Order Schemes
Author
J. Droniou
Copyright Year
2020
Book
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples

Print ISBN: 978-3-030-43650-6

Electronic ISBN: 978-3-030-43651-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43651-3_1

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