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High Order Interpolation Error Analysis Based on Triangular Interpolations

The interpolation errors are analyzed by applying the high order interpolation methods to plane waves. The interpolation regions are chosen based on the regions with the smallest errors. Numerical implementations for the right triangular, equilateral triangular and rectangular interpolations are performed. Numerical results show that the right triangular interpolation is the most efficient, and the equilateral triangular interpolation is the most accurate. The higher order of interpolations, the more saving in interpolation time in triangular interpolations.