Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter

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.

arXiv comment26 pages, 2 figures. arXiv admin note: text overlap with arXiv:2106.03339