A Babu\v{s}ka-Aziz type proof of the circumradius condition

TL;DR

This paper provides a Babuška-Aziz type proof of the circumradius condition, a generalization of the maximum angle condition, for polynomial interpolation errors on triangles.

Contribution

It introduces a new proof technique for the circumradius condition, extending the theoretical understanding of interpolation error bounds.

Findings

The circumradius condition is more general than the maximum angle condition.

A Babuška-Aziz type proof for the circumradius condition is established.

The proof enhances the theoretical foundation for polynomial interpolation on triangles.

Abstract

In this paper the error of polynomial interpolation of degree 1 on triangles is considered. The circumradius condition, which is more general than the maximum angle condition, is explained and proved by the technique given by Babu\v{s}ka-Aziz.