Lower bounds for piecewise polynomial approximations of oscillatory functions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912142558494720 |
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| author | Galkowski, Jeffrey |
| author_facet | Galkowski, Jeffrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04757 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lower bounds for piecewise polynomial approximations of oscillatory functions Galkowski, Jeffrey Numerical Analysis 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. |
| title | Lower bounds for piecewise polynomial approximations of oscillatory functions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2211.04757 |