Hybrid Nitsche method for distributed computing
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911367019102208 |
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| author | Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha |
| author_facet | Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha |
| contents | We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hybrid Nitsche method for distributed computing Gustafsson, Tom Hannukainen, Antti Kohonen, Vili Videman, Juha Numerical Analysis 65F55, 65N30, 65N55, 65Y05 We extend a distributed finite element method built upon model order reduction to arbitrary polynomial degree using a hybrid Nitsche scheme. The new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results. |
| title | Hybrid Nitsche method for distributed computing |
| topic | Numerical Analysis 65F55, 65N30, 65N55, 65Y05 |
| url | https://arxiv.org/abs/2504.05036 |