Efficient Triangular Interpolation Methods: Error Analysis and Applications

The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (rms) errors on the right triangular, equilateral triangular, and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and rms errors are directly proportional to the (p + 1)th power of kh for both 1-D and (2-D, bivariate) interpolations, where k...