| Autor: |
Yining Yang, Cao Wen, Yang Liu, Hong Li, Jinfeng Wang |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Communications in Analysis and Mechanics, Vol 16, Iss 1, Pp 24-52 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2836-3310 |
| DOI: |
10.3934/cam.2024002?viewType=HTML |
| Popis: |
In this article, a second-order time discrete algorithm with a shifted parameter $ \theta $ combined with a fast time two-mesh (TT-M) mixed finite element (MFE) scheme was considered to look for the numerical solution of the nonlinear fractional hyperbolic wave model. The second-order backward difference formula including a shifted parameter $ \theta $ (BDF2-$ \theta $) with the weighted and shifted Grünwald difference (WSGD) approximation for fractional derivative was used to discretize time direction at time $ t_{n-\theta} $, the $ H^1 $-Galerkin MFE method was applied to approximate the spatial direction, and the fast TT-M method was used to save computing time of the developed MFE system. A priori error estimates for the fully discrete TT-M MFE system were analyzed and proved in detail, where the second-order space-time convergence rate in both $ L^2 $-norm and $ H^1 $-norm were derived. Detailed numerical algorithms with smooth and weakly regular solutions were provided. Finally, some numerical examples were provided to illustrate the feasibility and effectiveness for our scheme. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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