A new geometric condition equivalent to the maximum angle condition for tetrahedrons

02/09/2021
by   Hiroki Ishizaka, et al.
0

For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant that is smaller than π. Then, it is said to satisfy the maximum angle condition with the constant. The maximum angle condition is important in the error analysis of Lagrange interpolation on tetrahedrons. This condition ensures that we can obtain an error estimation, even on certain kinds of anisotropic tetrahedrons. In this paper, using two quantities that represent the geometry of tetrahedrons, we present an equivalent geometric condition to the maximum angle condition for tetrahedrons.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/22/2020

General theory of interpolation error estimates on anisotropic meshes

We propose a general theory of estimating interpolation error for smooth...
07/03/2020

Ordinary Facet Angles of a Stroked Path Tessellated by Uniform Tangent Angle Steps Are Bounded by Twice the Step Angle

We explain geometrically why ordinary facet angles of a stroked path tes...
08/04/2020

Geometric Interpretations of the Normalized Epipolar Error

In this work, we provide geometric interpretations of the normalized epi...
06/03/2021

The Effect of Pore Structure in Flapping Wings on Flight Performance

This study investigates the effects of porosity on flying creatures such...
12/01/2021

Hyperbolae are the locus of constant angle difference

Given two points A,B in the plane, the locus of all points P for which t...
08/25/2021

What is most difficult for students in studying irregular triangles and solving trigonometry

Students who decide to choose the main subject of study of mathematics, ...
This week in AI

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