Work

Lower bounds for piecewise polynomial approximations of oscillatory functions

Year: 2024

Type: article

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.

Source: Journal of Approximation Theory

DOI: 10.1016/j.jat.2024.106100

Author: Jeffrey Galkowski

Institution: University College London

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,830

Funder: Engineering and Physical Sciences Research Council