A Recovery-Based Error Indicator for Finite Difference Methods
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914259335643136 |
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| author | Sindy, Ferhat Buffa, Annalisa Picasso, Marco |
| author_facet | Sindy, Ferhat Buffa, Annalisa Picasso, Marco |
| contents | A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable polynomial Finite Element space. A recovery-based error indicator, with the polynomial-preserving property, is then applied to estimate the gradient error. The performance and accuracy of the proposed error indicator are demonstrated through several numerical experiments, including the two-dimensional Poisson problem solved using second- and fourth-order finite difference schemes. Additional experiments are conducted on elliptic problems with discontinuous coefficients, as well as on the two and three-dimensional wave equation in homogeneous media with second- and fourth-order finite differences, and in heterogeneous media with second-order finite differences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11308 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Recovery-Based Error Indicator for Finite Difference Methods Sindy, Ferhat Buffa, Annalisa Picasso, Marco Numerical Analysis 65M06, 35L05 A novel recovery-based error indicator for high-order Finite Difference Methods, based on post-processing of the Finite Difference values is presented. The values obtained on the Finite Difference grid are interpolated into a suitable polynomial Finite Element space. A recovery-based error indicator, with the polynomial-preserving property, is then applied to estimate the gradient error. The performance and accuracy of the proposed error indicator are demonstrated through several numerical experiments, including the two-dimensional Poisson problem solved using second- and fourth-order finite difference schemes. Additional experiments are conducted on elliptic problems with discontinuous coefficients, as well as on the two and three-dimensional wave equation in homogeneous media with second- and fourth-order finite differences, and in heterogeneous media with second-order finite differences. |
| title | A Recovery-Based Error Indicator for Finite Difference Methods |
| topic | Numerical Analysis 65M06, 35L05 |
| url | https://arxiv.org/abs/2601.11308 |