Lower bounds for piecewise polynomial approximations of oscillatory functions
Numerical Analysis
2024-12-05 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2211.04757,
title = {Lower bounds for piecewise polynomial approximations of oscillatory functions},
author = {Jeffrey Galkowski},
journal= {arXiv preprint arXiv:2211.04757},
year = {2024}
}
Comments
Updated introductory material and made estimates p-explicit