Geodesic
Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation
Applications of Mathematics, Tome 61 (2016) no. 2, pp. 121-133

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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.
DOI : 10.1007/s10492-016-0125-y
Classification : 65D05, 65N30
Keywords: Lagrange interpolation; Babuška-Aziz's technique; difference quotients 
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Kobayashi, Kenta; Tsuchiya, Takuya. Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation. Applications of Mathematics, Tome 61 (2016) no. 2, pp. 121-133. doi: 10.1007/s10492-016-0125-y

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