Optimal error analysis of an interior penalty virtual element method for fourth-order singular perturbation problems
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912999813414912 |
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| author | Feng, Fang Sun, Yuanyi Yu, Yue |
| author_facet | Feng, Fang Sun, Yuanyi Yu, Yue |
| contents | In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning the perturbation parameter. However, the resulting uniform convergence rate is only of half-order, which is suboptimal. In this work, we demonstrate that the proposed IPVEM in fact achieves optimal and uniform error estimates, even in the presence of boundary layers. The theoretical results are substantiated through extensive numerical experiments, which confirm the validity of the error estimates and highlight the method's effectiveness for singularly perturbed problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal error analysis of an interior penalty virtual element method for fourth-order singular perturbation problems Feng, Fang Sun, Yuanyi Yu, Yue Numerical Analysis In recent studies \cite{ZZ24, FY24}, the Interior Penalty Virtual Element Method (IPVEM) has been developed for solving a fourth-order singular perturbation problem, with uniform convergence established in the lowest-order case concerning the perturbation parameter. However, the resulting uniform convergence rate is only of half-order, which is suboptimal. In this work, we demonstrate that the proposed IPVEM in fact achieves optimal and uniform error estimates, even in the presence of boundary layers. The theoretical results are substantiated through extensive numerical experiments, which confirm the validity of the error estimates and highlight the method's effectiveness for singularly perturbed problems. |
| title | Optimal error analysis of an interior penalty virtual element method for fourth-order singular perturbation problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.16070 |