A virtual element method on polyhedral meshes for the sixth-order elliptic problem
| Autor: | Dassi, Franco, Mora, David, Reales, Carlos, Velàsquez, Ivàn |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this work we analyze a virtual element method on polyhedral meshes for solving the sixth-order elliptic problem with simply supported boundary conditions. We apply the Ciarlet-Raviart arguments to introduce an auxiliary unknown $\sigma:=-\Delta^2 u$ and to search the main uknown $u$ in the $H^2\cap H_0^1$ Sobolev space. The virtual element discretization is well possed on a $C^1\times C^0$ virtual element spaces. We also provide the convergence and error estimates results. Finally, we report a series of numerical tests to verify the performance of numerical scheme. Comment: 20 pages 5 figures |
| Databáze: | arXiv |
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