We consider the approximation of (generalized) functions with continuous piecewise polynomials or with piecewise polynomials that are allowed to be discontinuous. Best error localization then means that the best error in the whole domain is equivalent to an appropriate accumulation of best errors in small domains, e.g., in mesh elements. We review and compare such best error localization in the three cases of the Sobolev-Hilbert triplet (H1 0 , L2 , H−1 ).
Best Error Localizations for Piecewise Polynomial Approximation of Gradients, Functions and Functionals / A. Veeser (LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING). - In: Numerical Mathematics and Advanced Applications ENUMATH 2017 / [a cura di] F. Radu, K. Kumar, I. Berre, J. Nordbotten, I. Pop. - Prima edizione. - [s.l] : Springer, Cham, 2019. - ISBN 9783319964140. - pp. 357-365 (( convegno ENUMATH 2017 tenutosi a Voss nel 2017 [10.1007/978-3-319-96415-7_31].
Best Error Localizations for Piecewise Polynomial Approximation of Gradients, Functions and Functionals
A. Veeser
2019
Abstract
We consider the approximation of (generalized) functions with continuous piecewise polynomials or with piecewise polynomials that are allowed to be discontinuous. Best error localization then means that the best error in the whole domain is equivalent to an appropriate accumulation of best errors in small domains, e.g., in mesh elements. We review and compare such best error localization in the three cases of the Sobolev-Hilbert triplet (H1 0 , L2 , H−1 ).
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