Instability of lagrange interpolation on H1(Ω) ∩ c(Ω)

Khan, MYF and Biswas, R and Sau, RC (2019) Instability of lagrange interpolation on H1(Ω) ∩ c(Ω). In: Mathematics Student, 88 (1-2). pp. 153-158.

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Abstract

It is known that the Lagrange interpolation is not defined for H1(Ω) functions. But, for functions in H1(Ω) ∩ C(Ω) point values are well defined and hence the Lagrange interpolation can be introduced. An important feature of an interpolation that many analysis require is its stability under some norm. In this article, we show that the Lagrange interpolation on the space H1(Ω) ∩ C(Ω) is not stable under the H1(Ω) norm by giving a counter example.

Item Type:	Journal Article
Publication:	Mathematics Student
Publisher:	Informatics Publishing Limited and The Indian Mathematical Society
Additional Information:	The copyright for this article belongs to Informatics Publishing Limited and The Indian Mathematical Society.
Keywords:	Lagrange interpolation; Sobolev spaces; Stability
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	05 Dec 2022 05:10
Last Modified:	05 Dec 2022 05:10
URI:	https://eprints.iisc.ac.in/id/eprint/78189

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