General theory of interpolation error estimates on anisotropic meshes, part II

06/07/2021
by   Hiroki Ishizaka, et al.
0

We present a general theory of interpolation error estimates for smooth functions and inverse inequalities on anisotropic meshes. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the two-dimensional case, our geometric parameter is equivalent to the circumradius of a triangle. In the three-dimensional case, our geometric parameter also represents the flatness of a tetrahedron. This paper also includes 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 2 was incorrect.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/05/2021

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

This paper presents delicate Raviart–Thomas interpolation error estimate...
02/22/2020

General theory of interpolation error estimates on anisotropic meshes

We propose a general theory of estimating interpolation error for smooth...
03/12/2021

Anisotropic H_div-norm error estimates for rectangular H_div-elements

For the discretisation of H_div-functions on rectangular meshes there ar...
01/14/2022

Error estimates for harmonic and biharmonic interpolation splines with annular geometry

The main result in this paper is an error estimate for interpolation bih...
05/25/2021

A DDR method for the Reissner-Mindlin plate bending problem on polygonal meshes

In this work we propose a discretisation method for the Reissner–Mindlin...
12/06/2016

Porous Structure Design in Tissue Engineering Using Anisotropic Radial Basis Function

Development of additive manufacturing in last decade greatly improves ti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.