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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24567 |
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| _version_ | 1866913065616801792 |
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| author | Li, Fei Hong, Qingguo Tang, Ming Zhong, Liuqiang |
| author_facet | Li, Fei Hong, Qingguo Tang, Ming Zhong, Liuqiang |
| contents | We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and Zhang [SIAM J. Sci. Comput., 43 (2021), pp. A908-A928], which is restricted to symmetric positive-definite problems, the proposed method introduces an additional correction step that solves a small-scale discrete residual problem on the coarse mesh. This step entails negligible additional computational cost and allows us to show that the L2-norm error of the corrected discrete solution is a higher-order of the energy-norm error of the discrete solution. Using this result, we prove a contraction property for a suitable sum of quasi-errors on two successive adaptive meshes and establish convergence of the method. Numerical experiments illustrate the improved effectiveness and robustness of our method in comparison with ATGFEM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems Li, Fei Hong, Qingguo Tang, Ming Zhong, Liuqiang Numerical Analysis We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and Zhang [SIAM J. Sci. Comput., 43 (2021), pp. A908-A928], which is restricted to symmetric positive-definite problems, the proposed method introduces an additional correction step that solves a small-scale discrete residual problem on the coarse mesh. This step entails negligible additional computational cost and allows us to show that the L2-norm error of the corrected discrete solution is a higher-order of the energy-norm error of the discrete solution. Using this result, we prove a contraction property for a suitable sum of quasi-errors on two successive adaptive meshes and establish convergence of the method. Numerical experiments illustrate the improved effectiveness and robustness of our method in comparison with ATGFEM. |
| title | A correction adaptive two-grid finite element method for nonselfadjoint or indefinite elliptic problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.24567 |