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interpolation error estimate

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Interpolation of non-smooth functions on anisotropic finite element meshes
Thomas Apel
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 6 / November 1999

Published online by Cambridge University Press:

15 August 2002, pp. 1149-1185

Print publication:

November 1999
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In this paper, several modifications of the quasi-interpolationoperator of Scott andZhang [30]are discussed. The modified operators are defined for non-smooth functionsand are suited for application on anisotropic meshes. Theanisotropy of the elements is reflected in the local stability andapproximation error estimates.As an application, an example is considered where anisotropic finiteelement meshes are appropriate, namely the Poisson problem in domainswith edges.