Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation
In this paper, we present and analyze two linearized Galerkin finite element schemes, which are constructed by employing the H2N2 formula and its fast version in time direction, for solving the nonlinear time-fractional diffusion-wave equation. By utilizing mathematical induction, the optimal error...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-08-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000353 |
| _version_ | 1797727639709941760 |
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| author | Zhen Guan Jungang Wang Ying Liu Yufeng Nie |
| author_facet | Zhen Guan Jungang Wang Ying Liu Yufeng Nie |
| author_sort | Zhen Guan |
| collection | DOAJ |
| description | In this paper, we present and analyze two linearized Galerkin finite element schemes, which are constructed by employing the H2N2 formula and its fast version in time direction, for solving the nonlinear time-fractional diffusion-wave equation. By utilizing mathematical induction, the optimal error estimates in H1-norm are derived without any ratio restrictions between the time step size τ and the space mesh size h. The key point in our argument is the application of Sobolev’s embedding inequality to the fully discrete solution uhn. On the other hand, additional time-discrete elliptic system and the inverse inequality, which play a vital role in the temporal–spatial error splitting technique, are avoided in our numerical analysis. Finally, two numerical experiments are given to demonstrate the theoretical findings. |
| first_indexed | 2024-03-12T11:02:31Z |
| format | Article |
| id | doaj.art-72385ee36a2f44979fe5965ccc201943 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-03-12T11:02:31Z |
| publishDate | 2023-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-72385ee36a2f44979fe5965ccc2019432023-09-02T04:32:16ZengElsevierResults in Applied Mathematics2590-03742023-08-0119100389Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equationZhen Guan0Jungang Wang1Ying Liu2Yufeng Nie3School of Mathematics and Statistics, Pingdingshan University, Pingdingshan, 467000, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, China; Corresponding author.Department of Mathematics, School of Science, Xi’an University of Technology, Xi’an, 710048, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710129, ChinaIn this paper, we present and analyze two linearized Galerkin finite element schemes, which are constructed by employing the H2N2 formula and its fast version in time direction, for solving the nonlinear time-fractional diffusion-wave equation. By utilizing mathematical induction, the optimal error estimates in H1-norm are derived without any ratio restrictions between the time step size τ and the space mesh size h. The key point in our argument is the application of Sobolev’s embedding inequality to the fully discrete solution uhn. On the other hand, additional time-discrete elliptic system and the inverse inequality, which play a vital role in the temporal–spatial error splitting technique, are avoided in our numerical analysis. Finally, two numerical experiments are given to demonstrate the theoretical findings.http://www.sciencedirect.com/science/article/pii/S2590037423000353Linearized Galerkin FEMsH2N2 formulaNonlinear time-fractional diffusion-wave equationUnconditionally optimal error estimatesSobolev’s embedding inequality |
| spellingShingle | Zhen Guan Jungang Wang Ying Liu Yufeng Nie Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation Results in Applied Mathematics Linearized Galerkin FEMs H2N2 formula Nonlinear time-fractional diffusion-wave equation Unconditionally optimal error estimates Sobolev’s embedding inequality |
| title | Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation |
| title_full | Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation |
| title_fullStr | Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation |
| title_full_unstemmed | Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation |
| title_short | Unconditional convergence analysis of two linearized Galerkin FEMs for the nonlinear time-fractional diffusion-wave equation |
| title_sort | unconditional convergence analysis of two linearized galerkin fems for the nonlinear time fractional diffusion wave equation |
| topic | Linearized Galerkin FEMs H2N2 formula Nonlinear time-fractional diffusion-wave equation Unconditionally optimal error estimates Sobolev’s embedding inequality |
| url | http://www.sciencedirect.com/science/article/pii/S2590037423000353 |
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