Smoother-type a posteriori error estimates for finite element methods
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911462020087808 |
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| author | Li, Yuwen Shui, Han |
| author_facet | Li, Yuwen Shui, Han |
| contents | This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary finer mesh to process the finite element residual for a posteriori error control. The implementation has linear complexity and requires only a coarse-to-fine prolongation operator. For symmetric problems, we prove the reliability and efficiency of smoother-type error estimators under a saturation assumption. Numerical experiments for various PDEs demonstrate that the proposed smoother-type error estimators outperform residual-type estimators in accuracy and exhibit robustness with respect to parameters and polynomial degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smoother-type a posteriori error estimates for finite element methods Li, Yuwen Shui, Han Numerical Analysis This work develops user-friendly a posteriori error estimates of finite element methods, based on smoothers of linear iterative solvers. The proposed method employs simple smoothers, such as Jacobi or Gauss-Seidel iteration, on an auxiliary finer mesh to process the finite element residual for a posteriori error control. The implementation has linear complexity and requires only a coarse-to-fine prolongation operator. For symmetric problems, we prove the reliability and efficiency of smoother-type error estimators under a saturation assumption. Numerical experiments for various PDEs demonstrate that the proposed smoother-type error estimators outperform residual-type estimators in accuracy and exhibit robustness with respect to parameters and polynomial degrees. |
| title | Smoother-type a posteriori error estimates for finite element methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.07677 |