English

Anisotropic interpolation error estimates using a new geometric parameter

Numerical Analysis 2022-08-03 v3 Numerical Analysis

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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Cite

@article{arxiv.2106.03339,
  title  = {Anisotropic interpolation error estimates using a new geometric parameter},
  author = {Hiroki Ishizaka and Kenta Kobayashi and Takuya Tsuchiya},
  journal= {arXiv preprint arXiv:2106.03339},
  year   = {2022}
}

Comments

36 pages, 12 figures