Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption, Part 2: Lagrange interpolation on tetrahedrons

2021/03/15 by Kobayashi, Kenta, Tsuchiya, Takuya
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2103.08101

Abstract

This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In this manuscript, we explain the error analysis of Lagrange interpolation on (possibly anisotropic) tetrahedrons. The manuscript is not intended to be a research paper. We hope that, in the future, it will be merged into a textbook on the mathematical theory of the finite element methods.

Related

• Error Analysis of Lagrange Interpolation on Tetrahedrons
• General theory of interpolation error estimates on anisotropic meshes
• Average Interpolation Under the Maximum Angle Condition
• Interpolation error analysis using a new geometric parameter
• Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra