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Keywords:
quadratic Lagrange interpolation in 2D; stability
quadratic Lagrange interpolation in 2D; stability
Summary:
An explicit description of the basic Lagrange polynomials in two variables related to a six-tuple $a^1,\dots ,a^6$ of nodes is presented. Stability of the related Lagrange interpolation is proved under the following assumption: $a^1,\dots ,a^6$ are the vertices of triangles $T_1,\dots ,T_4$ without obtuse inner angles such that $T_1$ has one side common with $T_j$ for $j=2,3,4$.
References:
[1] Dalík, J.: Quadratic interpolation polynomials in vertices of strongly regular triangulations. in Finite Element Methods, superconvergence, post-processing and a posteriori estimates, Ed. Křižek, Neittaanmäki, Stenberg, Marcel Dekker (1996), 85–95. MR 1602833
[2] Sauer, T., Xu, Y.: On multivariate Lagrange interpolation. Math. of Comp. 64 (1995), 1147–1170. MR 1297477
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