Optimal Superconvergence Analysis for the Crouzeix-Raviart and the Morley elements
| Autor: | Hu, Jun, Ma, Limin, Ma, Rui |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, an improved superconvergence analysis is presented for both the Crouzeix-Raviart element and the Morley element. The main idea of the analysis is to employ a discrete Helmholtz decomposition of the difference between the canonical interpolation and the finite element solution for the first order mixed Raviart--Thomas element and the mixed Hellan--Herrmann--Johnson element, respectively. This, in particular, allows for proving a full one order superconvergence result for these two mixed finite elements. Finally, a full one order superconvergence result of both the Crouzeix-Raviart element and the Morley element follows from their special relations with the first order mixed Raviart--Thomas element and the mixed Hellan--Herrmann--Johnson element respectively. Those superconvergence results are also extended to mildly-structured meshes. Comment: 20 pages, 3 figures, 3 tables. arXiv admin note: text overlap with arXiv:1802.01896 |
| Databáze: | arXiv |
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