Abstract
We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates on squeezed triangles and tetrahedrons are proved by a method that is a straightforward extension of the original one given by Babuška-Aziz.
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Cordially dedicated to Prof. Ivo Babuška on the occasion of his 90th birthday.
The authors are supported by JSPS Grant-in-Aid for Scientific Research (C) 25400198 and (C) 26400201. The second author is partially supported by JSPS Grant-in-Aid for Scientific Research (B) 23340023.
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Kobayashi, K., Tsuchiya, T. Extending Babuška-Aziz’s theorem to higher-order Lagrange interpolation. Appl Math 61, 121–133 (2016). https://doi.org/10.1007/s10492-016-0125-y
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DOI: https://doi.org/10.1007/s10492-016-0125-y