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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/2605.30037 |
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| _version_ | 1866916061550477312 |
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| author | Gao, Mengxue Su, Bing Zhou, Jianwei |
| author_facet | Gao, Mengxue Su, Bing Zhou, Jianwei |
| contents | A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical analysis and confirm the high efficiency and accuracy of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A novel mixed spectral method with ball polynomials for the Biharmonic equation on a unit ball Gao, Mengxue Su, Bing Zhou, Jianwei Numerical Analysis 65M70, 65N35 A novel mixed spectral-Galerkin method based on generalized ball polynomials is proposed for solving the biharmonic equation on a unit ball. By introducing an auxiliary variable to decouple the biharmonic equation into a system of second-order equations, the corresponding discrete scheme yields a strictly diagonal stiffness matrix, which significantly enhances the computational efficiency. Rigorous a-priori error estimates are established to demonstrate the exponential convergence rates in both the $L^2$- and $H^1$-norms. Extensive numerical experiments are conducted to verify the theoretical analysis and confirm the high efficiency and accuracy of the proposed scheme. |
| title | A novel mixed spectral method with ball polynomials for the Biharmonic equation on a unit ball |
| topic | Numerical Analysis 65M70, 65N35 |
| url | https://arxiv.org/abs/2605.30037 |