Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866908175149563904 |
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| author | Dong, Guozhi Guo, Hailong Shi, Zuoqiang |
| author_facet | Dong, Guozhi Guo, Hailong Shi, Zuoqiang |
| contents | This paper is dedicated to the development of numerical analysis for high-order methods solving partial differential equations on scattered point clouds. We build a novel geometric error analysis framework by estimating the error in the approximation of the Riemann metric tensor. The innovative framework serves as a fundamental tool for analyzing discontinuous Galerkin methods applied to the Laplace-Beltrami operator on possibly discontinuous geometry. We provide numerical examples on patchy surfaces reconstructed from point clouds to support our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_15433 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud Dong, Guozhi Guo, Hailong Shi, Zuoqiang Numerical Analysis 65D18, 65N12, 65N25, 65N30, 68U05 This paper is dedicated to the development of numerical analysis for high-order methods solving partial differential equations on scattered point clouds. We build a novel geometric error analysis framework by estimating the error in the approximation of the Riemann metric tensor. The innovative framework serves as a fundamental tool for analyzing discontinuous Galerkin methods applied to the Laplace-Beltrami operator on possibly discontinuous geometry. We provide numerical examples on patchy surfaces reconstructed from point clouds to support our theoretical findings. |
| title | Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud |
| topic | Numerical Analysis 65D18, 65N12, 65N25, 65N30, 68U05 |
| url | https://arxiv.org/abs/2012.15433 |