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Foundations of Computational Mathematics
Erschienen in: Foundations of Computational Mathematics 3/2016

01.06.2016

Approximating Gradients with Continuous Piecewise Polynomial Functions

verfasst von: Andreas Veeser

Erschienen in: Foundations of Computational Mathematics | Ausgabe 3/2016

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Abstract

Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is that the global best approximation error is equivalent to an appropriate sum in terms of the local best approximation errors on elements. Thus, requiring continuity does not downgrade local approximation capability and discontinuous piecewise polynomials essentially do not offer additional approximation power, even for a fixed mesh. This result implies error bounds in terms of piecewise regularity over the whole admissible smoothness range. Moreover, it allows for simple local error functionals in adaptive tree approximation of gradients.
Vorheriger Artikel Reconstruction of Signals from Magnitudes of Redundant Representations: The Complex Case
Nächster Artikel Numerical Stability in the Presence of Variable Coefficients

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Metadaten
Titel
Approximating Gradients with Continuous Piecewise Polynomial Functions
verfasst von
Andreas Veeser
Publikationsdatum
01.06.2016
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 3/2016
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-015-9262-z

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