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

2021/10/05 by Hiroki Ishizaka, Ishizaka, Hiroki · 1 citation
Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2110.02348

openalex publication_date 2021/10/05 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

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.

Citations

• Polynomial approximation of functions in Sobolev spaces

Cited by

• On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition

Related

• Anisotropic interpolation error estimates using a new geometric parameter
• General theory of interpolation error estimates on anisotropic meshes
• Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
• Anisotropic interpolation error estimate for arbitrary quadrilateral\n isoparametric elements
• Interpolation error analysis using a new geometric parameter