Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter
Hiroki Ishizaka
TL;DR
This paper introduces a new geometric parameter for simplices to derive precise anisotropic Raviart-Thomas interpolation error estimates on anisotropic meshes, correcting previous theoretical inaccuracies.
Contribution
It proposes a novel geometric parameter for simplices enabling improved anisotropic interpolation error estimates and corrects prior theoretical errors in existing literature.
Findings
New anisotropic Raviart-Thomas error estimates derived
Introduction of a geometric parameter for simplices
Correction of previous theoretical inaccuracies
Abstract
We present precise Raviart-Thomas interpolation error estimates on anisotropic meshes. The novel aspect of our theory is the introduction of a new geometric parameter of simplices. It is possible to obtain new anisotropic Raviart-Thoma error estimates using the parameter. We also include corrections to an error in "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191), in which Theorem 3 was incorrect.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Advanced Numerical Analysis Techniques · Numerical methods in engineering