On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915851436818432 |
|---|---|
| author | Smears, Iain |
| author_facet | Smears, Iain |
| contents | For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the error, when considering the numerical solution as the average between the usual continuous piecewise affine-in-time and piecewise constant-in-time reconstructions. This illustrates how the efficiency of the estimators is not only possibly dependent on the choice of norm, but also on the choice of notion of numerical solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13188 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm Smears, Iain Numerical Analysis For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the error, when considering the numerical solution as the average between the usual continuous piecewise affine-in-time and piecewise constant-in-time reconstructions. This illustrates how the efficiency of the estimators is not only possibly dependent on the choice of norm, but also on the choice of notion of numerical solution. |
| title | On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.13188 |