A counterexample to a result concerning controlled approximation

Jia, Rong Qing

doi:10.1090/S0002-9939-1986-0845982-1

A counterexample to a result concerning controlled approximation
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by Rong Qing Jia PDF

Proc. Amer. Math. Soc. 97 (1986), 647-654 Request permission

Abstract:

A result of Strang and Fix states that if the order of controlled approximation from a collection of locally supported elements is $k$, then there is a linear combination $\Omega$ of those elements and their translates such that any polynomial of degree less than $k$ can be reproduced by $\Omega$ and its translates. This paper gives a counterexample to their result.

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A Fourier analysis of the finite element variational method