A priori error estimates for Lagrange interpolation on 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.

15 pages, 2 figures To appear in Applications of Mathematics

References in corpus (2)

• A Babuška-Aziz type proof of the circumradius condition
• On the circumradius condition for piecewise linear triangular elements

Cited by in corpus (7)

• A new geometric condition equivalent to the maximum angle condition for tetrahedrons
• Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods
• Extenting of Babuška-Aziz's theorem to higher-order Lagrange interpolation
• Approximating surface areas by interpolations on triangulations
• A robust discontinuous Galerkin scheme on anisotropic meshes
• Error Analysis of Lagrange Interpolation on Tetrahedrons
• General theory of interpolation error estimates on anisotropic meshes