Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911063907237888 |
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| author | Faria, Luiz Maltez Marchand, Pierre Montanelli, Hadrien |
| author_facet | Faria, Luiz Maltez Marchand, Pierre Montanelli, Hadrien |
| contents | We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations Faria, Luiz Maltez Marchand, Pierre Montanelli, Hadrien Numerical Analysis We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency errors introduced by the perturbed bilinear and sesquilinear forms. We illustrate our results with numerical experiments in 3D based on basis functions and curved triangular elements up to order four. |
| title | Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.13955 |