A priori error estimates for Lagrange interpolation on triangles

TL;DR

This paper derives new a priori error estimates for Lagrange interpolation on triangles, relating the error bounds to geometric properties like diameter and circumradius without imposing geometric constraints.

Contribution

It introduces a novel a priori error estimate for Lagrange interpolation on triangles based on diameter and circumradius, removing geometric restrictions.

Findings

Error bounds expressed in terms of diameter and circumradius

No geometric conditions needed for the estimates

Enhances understanding of interpolation accuracy on arbitrary triangles

Abstract

We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates.