Abstract
In this paper, we propose an improved interpolation error estimate based on a new Taylor-like formula, which we apply to the finite element method. We first present a new first-order and second-order expansion formula with a reduced remainder. Then, we derive a new interpolation error estimate in W1,p. We compare this with the classical error estimates based on the standard Taylor formula and the corresponding interpolation error estimate derived from the mean value theorem. We illustrate, with examples, the significant reduction this yields in finite element computation costs.
| Original language | English |
|---|---|
| Title of host publication | New Trends in the Applications of Differential Equations in Sciences - NTADES 2024 |
| Editors | Angela Slavova |
| Publisher | Springer |
| Pages | 277-290 |
| Number of pages | 14 |
| ISBN (Print) | 9783031833977 |
| DOIs | |
| State | Published - 2025 |
| Externally published | Yes |
| Event | 11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024 - Saints Constantine and Helena, Bulgaria Duration: 7 Jul 2024 → 10 Jul 2024 |
Publication series
| Name | Springer Proceedings in Mathematics and Statistics |
|---|---|
| Volume | 488 |
| ISSN (Print) | 2194-1009 |
| ISSN (Electronic) | 2194-1017 |
Conference
| Conference | 11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024 |
|---|---|
| Country/Territory | Bulgaria |
| City | Saints Constantine and Helena |
| Period | 7/07/24 → 10/07/24 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
Keywords
- Approximation error
- Finite elements
- Interpolation error
- Taylor-like formula
- Taylor’s theorem