The TRUNC element in any dimension and application to a modified Poisson equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916377291390976 |
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| author | Li, Hongliang Ming, Pingbing Zhou, Yinghong |
| author_facet | Li, Hongliang Ming, Pingbing Zhou, Yinghong |
| contents | We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The TRUNC element in any dimension and application to a modified Poisson equation Li, Hongliang Ming, Pingbing Zhou, Yinghong Numerical Analysis We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions. |
| title | The TRUNC element in any dimension and application to a modified Poisson equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.00748 |