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

10/05/2021

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by   Hiroki Ishizaka, et al.

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This paper presents delicate Raviart–Thomas interpolation error estimates on anisotropic meshes. The novel aspect of our theory is the introduction of a new geometric parameter of simplices, and we show the stability of global Raviart–Thomas interpolation in terms of the geometric 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.