Anisotropic interpolation error estimates using a new geometric parameter
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
TL;DR
This paper introduces new anisotropic interpolation error estimates based on a novel geometric parameter, providing bounds that depend on simplex diameter and geometric properties, with corrections to previous results.
Contribution
It develops a new framework for anisotropic interpolation error estimates using a geometric parameter, improving upon prior theories and correcting earlier errors.
Findings
Derived bounds for interpolation errors involving geometric parameters
Established inverse inequalities on anisotropic meshes
Corrected previous theoretical inaccuracies
Abstract
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the diameter of a simplex and the geometric parameter. Imposing additional assumptions makes it possible to obtain anisotropic error estimates. This paper also includes corrections to an error in Theorem 2 of our previous paper, "General theory of interpolation error estimates on anisotropic meshes" (Japan Journal of Industrial and Applied Mathematics, 38 (2021) 163-191).
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Numerical Analysis Techniques · Advanced Numerical Methods in Computational Mathematics