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Lower bounds for piecewise polynomial approximations of oscillatory functions

Galkowski, Jeffrey; (2025) Lower bounds for piecewise polynomial approximations of oscillatory functions. Journal of Approximation Theory , 305 , Article 106100. 10.1016/j.jat.2024.106100. (In press). Green open access

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Abstract

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when the polynomial degree is fixed. These lower bounds, for example, apply when approximating solutions to Helmholtz plane wave scattering problem.

Type: Article
Title: Lower bounds for piecewise polynomial approximations of oscillatory functions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jat.2024.106100
Publisher version: http://dx.doi.org/10.1016/j.jat.2024.106100
Language: English
Additional information: © 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Keywords: Science & Technology, Physical Sciences, Mathematics, FINITE-ELEMENT SOLUTION, HIGH WAVE-NUMBER, HELMHOLTZ-EQUATION, CONVERGENCE ANALYSIS, DISCRETIZATIONS, VERSION
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10198786
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