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quadratic Lagrange finite elements in 1D; local interpolation of functions in one variable
We analyse the error of interpolation of functions from the space $H^3(a,c)$ in the nodes $a<b<c$ of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes $a,b,c$ change as the length of interval $[a,c]$ approaches zero.
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